Explain the process of solving inequality with variables on both sides. Show an example.

Answers

Answer 1

Answer:

Inequalities work exactly like equations with one exception. The process begins just like equations: first, do the opposite of what you see, then do the same thing on the other side of the sign. At the last step of solving an inequality, if you multiply or divide by a negative number, then you reverse the sign

Answer 2

The two examples show the process of solving inequality with variables on both sides are

3 + x > 3x - 6

3 - 4x < 2x + 8

The process is shown below.

What is inequality?

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

Let us consider an inequality:

3 + x > 3x - 6 ____(1)
3 - 4x < 2x + 8 _____(2)

We will solve for x.

From (1),

3 + x > 3x - 6

Subtract 3 on both sides.

3 + x - 3 > 3x - 6 - 3

x > 3x - 9

Add 9 on both sides.

x + 9 > 3x - 9 + 9

x + 9 > 3x

Subtract x on both sides.

x + 9 - x > 3x - x

9 > 2x

Divide 2 on both sides.

9/2 > x

x < 9/2

This means that x must be less than 9/2.

From (2),

3 - 4x < 2x + 8

Subtract 3 on both sides.

3 - 4x - 3 < 2x + 8 - 3

- 4x < 2x + 5

Subtract -2x on both sides.

-4x - 2x < 2x + 5 - 2x

-6x < 5

Divide both sides by 6.

-x < 5/6

Since we can not keep a negative sign with x we will multiply a negative on both sides and flip the inequality.

- (-x) > -5/6

x > -5/6

Thus,

The two examples show the process of solving inequality with variables on both sides are:

3 + x > 3x - 6

= x < 9/2


3 - 4x < 2x + 8

= x > -5/6

Learn more about inequalities here:

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Related Questions

Look at the picture.

Answers

Answer:

178.5

Step-by-step explanation:

First, you take 8*10 and the subtract 7. Second, because it is a fraction, you divide it by 4*10-4. Basally,  its 8*10=80-7/4*10=40-4

What is the Law of Exponents?

Answers

Answer:

The exponent of a number says how many times to use the number in a multiplication.

Example:

[tex]8^{2}[/tex] = 8 × 8 = 64

PLS HELP NEEDED TODAY

Answers

A: 4 percent - 4% + 98 = 101.92

B:

Way One: 110 times 0.10 is 11. 110 - 11 = 99
Way Two: 110 times 0.90 is 99

C: yes, it would make sense to switch to company B because they have a lower price after discount.

Find the slope...........

Answers

First thing to do is find out the coordinates of two points on the graph (I will use the ones that have been marked by the red dots):

Point A: (3, -1)
Point B: (1, 2)

Then we will use the slope formula to work out the slope:

y₂ - y₁ / x₂ - x₁

Substitute in our points:

2 - (-1) / 1 - 3

Then we work out the expression (remember a negative and a negative make a positive!):

3 / -2

Then we check if we can simplify this fraction, which in this case we cannot.

Therefore the slope of that line would be:

3 / -2

(remember to write it as a fraction!)

Please help me i dont understand
At the start of the month, the value of Susan’s checking account was $53. She gets paid $375 per week for 4 weeks and spends $172 on groceries for the month. How much does Susan have in her checking account at the end of the month?

Answers

$1,381

Because 375×4= 1,500
and 1,500-172= 1,328
lastly, 1,328 + 53= 1,381
Susan has $1381.

[ 53 + (375x4) ] - 172

help please!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

18. slope =1/2 y-int= -6

19. slope=2 y-int= 8

Step-by-step explanation:

The slope for number 18 would be 1/2 and the y intercept would be -6

The slope for 19 would be 2 and I cannot see the picture of the intercept correctly, but I’m assuming it is 6

Simplify the expression 6(11+4−7h)

Answers

Answer:

−42h+90

Explanation:

6(11+4−7h)

=(6)(11+4+−7h)

=(6)(11)+(6)(4)+(6)(−7h)

=66+24−42h

=−42h+90

The answer is 90-42h

Please help!!! Will try my best to give brainliest!!!!


Find the GCF of n 3t ^2 and nt 4.


n ^3t^ 6

n ^3t ^4

nt ^2

n^ 4t^ 6

Answers

Answer: nt ^ 2
:))))

Answer:

for this question is nt^2 or C

Step-by-step explanation:

(MARKING) How many solutions does this equasion have? -4 - 10n = 8h + 10
ANSWER CHOICES
1. No solutions
2. One solution
3. Infinite solutions
Please answer soon will mark!

Answers

Answer:

infiintie\

Step-by-step explanation:

Answer:

3rd choice is your answer

Step-by-step explanation:

pls help me i dont understand it.....................

Answers

Brainliest pls






To the person above me :)

Is the table above proportional or non-proportional?

Answers

Answer: I think you should divide them all and if you get the same answer it’s proportional if you don’t get the same answer it’s non-proportional

Step-by-step explanation:

Answer:

It is non-proportional.

Step-by-step explanation:

The table is non-proportional because it expresses a curved line instead of a straight line.

base= 1.5 area=2 but what does height equal

Answers

I think the answer is 3

Answer:

i think its 1.33 repeating

Step-by-step explanation:

Solve the inequality $-4x > -24.$ Give your answer in interval notation.

Answers

Answer:

(negative infinity, 6)

Step-by-step explanation:

To get this:

1. -4x > 24

Divide by -4

2. x < 6

When you divide by a negative you have to flip the inequality. Therefore, any number that is less than 6 is the answer.

The solution of the inequality will be;

⇒ x ∈ (- ∞, 6)

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ - $4x > - $24

Now,

Solve the inequality as;

The inequality is,

⇒ - $4x > - $24

Multiply by - 1, we get;

⇒ $4x <  $24

Divide by 4, we get;

⇒ x < 6

⇒ x ∈ (- ∞, 6)

Thus, The solution of the inequality will be;

⇒ x ∈ (- ∞, 6)

Learn more about the inequality visit:

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The perimeter of the original rectangle on the left is 30 meters. The perimeter of the reduced rectangle on the right is 24 meters. What is x, the width of the original rectangle on the left? Round to the nearest hundredth if necessary.

A) 5 meters
B) 8 meters
C) 10 meters
D) 12 meters

Answers

X=5



Explanation:


If the triangle on the rights perimeter is 24 and two of the lengths are 8 then we know 8+8=16 24-16=8 8/2=4
So the triangle on the right has the numbers 8 and 4 as it’s length and width

So then you would find out how much it was dilated to get from 30 to 24
30/24 and you get 1.25 so you multiply 4 by 1.25 and get 5, and then to double check you can multiply 8 by 1.25 and get 10 then add it all together
5+5+10+10=30 so you know that’s correct.

Simplify (6^-8)^4 Please help

Answers

Answer:

6⁻³²  (or 1/6³²)

Step-by-step explanation:

(6⁻⁸) ⁴

= 6 ⁽⁻⁸⁾⁽⁴⁾

= 6⁻³²  ( or in fraction form 1/6³²)

Answer:

[tex]\frac{1}{6^{32} }[/tex]

Step-by-step explanation:

If I read the question rights its = [tex](6^{-8} )(^{4})[/tex]

what does tempature measure

Answers

Answer:

Temperature is a measure of the average kinetic energy of the particles in an object.

Step-by-step explanation:

which means its b

Look at the picture.

Answers

Answer:

boi

Step-by-step explanation:

Answer:THE ANSWER IS 3x10^30

Step-by-step explanation:

Write or draw TWO (2) DIFFERENT fractions that are equivalent to 5/6

Answers

You could do 10/12 and you could do 15/18


Hope that helps!

1/2(12w+8) -1/5(10w-5) find the difference

Answers

1/2(12w+8) -1/5(10w-5) = 4w + 3 or 4w + 5

( im kinda confused on this myself)

Answer: 4w + 5
(extra characters)

Assume that the cheetah travels an average of 40 mph to go from its resting place to a rock near a river. On the return trip to its resting place, the cheetah travels an average of 70 mph. If the cheetah traveled for 15 minutes, how many minutes did the return trip take to the nearest minute and second?
Set up the table as follows. Label the rows “To the River” and “From the River.” Label the columns “Distance,” “Rate,” and “Time (in Hours).” Let t represent the unknown quantity in the problem. Fill in the table.

Answers

Answer:

9.55 minutes

Step-by-step explanation:

x hours to go to the river

0.25-x hours to come back, since 15 minutes is 0.25 hr.

to the river 40 mph * x hours =40x miles

from the river 70 mph (0.25-x) hours=17.5-70x

those two are equal

40x=17.5-70x

110x=17.5

x=17.5/110=0.159 hours

9.55 minutes

Help, this is so confusing.

Answers

Answer:

D. $0.05

Step-by-step explanation:

Don't worry! I'll help you through it.

So we just have to find the unit rate (price) per apple.

$4 divided by 5lbs bag = $0.80 so, The 1st bag is $0.80 an apple.

$6 bag divided by 8lb = $0.75 an apple.

Now, simply subtract

0.80

-0.75

0.05

So your answer is D, $0.05

Have a great day!

~PumpkinSpice1

0.05 is the answer because the unit rates are 0.8 and 0.75

Which situation represents a proportional relationship?

a
The cost of purchasing a basket of oranges for $1.30 per pound plus $5.00 for the basket.
b
The cost of purchasing grapefruit for $1.80 per pound with a coupon for $1.00 off the total cost.
c
The cost of purchasing apples for $1.75 per pound plus a shipping fee of $0.16 per pound.
d
The cost of purchasing peaches for $7.00 per box of peaches with a delivery charge of $3.00.

Answers

I’m pretty sure it is C? But I’m not 100% sure
I think its either c or d im not sure though but it might be c

When two factors have opposite signs, is the product negative or positive??

Answers

Answer:

Negative

Step-by-step explanation:

If two signs differ the answer will always be negative. but if they are the same then the answer would be positive. Hope this helped!

Answer:

Negative

Hope this helped :)

Could someone please find the rate and y-intercept for these two points? (2,2) and (3,4) the help would be greatly appreciated!!

Answers

First use a formula to find rate of change
so a formula most commonly used is (y^1-y^2)/(x^1-x^2)

m= (y^1-y^2)/(x^1-x^2)
=m=(4-2)/(3-2)
=m=2/1
2/1 can also be expressed as just 2 since anything divided by 1 is just itself

Now use the formula y=mx+b to find the y intercept

use either of your two given point to susitute y and x

y=mx+b
Substitute your values
=(4)=(2)(3)+b
Calculate
=4=6+b
Subtract both sides by 6
=-2=b

Therefore the rate of change is 2/1 and the y-intercept is -2

please help I hate imagine math its in the photo ​

Answers

I wish I can help you
I’m so sorry but I have no idea

Slope-intercept form
find out the y intercept and slope

Answers

Answer:

18. Slope (m) = 1/2

Y-intercept (b) = -6

19. Slope (m) = 2

Y-intercep (b) = 8

20. y = 1/2 + 6

Step-by-step explanation:

y = mx + b

y - 2x = 8

y = 2x + 8

18.slope (m) = 1/2
Y - intercept

A fruit basket contains only apples and bananas. If there are 8 apples and 13 bananas, what is the ratio of bananas to fruit? Select all that apply. 13:8

Answers

Answer:

The ratio of bananas to total fruit is 13:21

Step-by-step explanation:

Since we already know the amount of apples and pears, we can find the total. 13+8=21, and since we know the number of pears, 13, we can say that the ratio is 13:21.

Answer: 13:21

13:21 is the correct answer I hope it helps

The temperature was -10 Fahrenheit at 8:00 PM one day in Denver. A cold front lowered the temperature over the next hour by 3 degrees. What was the new temperature at 9:00 PM?

Answers

Answer:

-13 degrees Fahrenheit

Step-by-step explanation:

3 degrees lower then -10 degrees would be -13.

Answer:

-13 Fahrenheit

Step-by-step explanation:

help meeee please HELPPPPPPPP

Answers

No the mixtures are not the same shade of purple. The reason is because when both mixtures use 21 cups of red paints the original recipe uses 14 cups of blue paint, while the new mixtures uses 15 cups if blue paint, Therefore the New Mixture would be more blue than the Original mixture

Answer:

they are different because the original paint goes 123456 and the new pait goes 246810.

Step-by-step explanation:

hope this helps!

please help! i’m having a rough time on this, could someone answer this question?

Answers

Answer:

y= -18

a= -18

Step-by-step explanation:

2y+3 = 3(y+7)

2y+3=3y+21

     -21     -21

2y-18=3y

-2y      -2y

-18=y

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