2x - 1 < 4
First, let's add 1 to both sides.
2x < 5
Divide both sides by 2
x < 5/2 or (-∞, [tex]\frac{5}{2}[/tex])
-5x - 3 > -3
Add 3 to both sides.
-5x > 0
Divide both sides by -5
x < 0 or (-∞, 0)
The solution set of the given set of linear inequations 2x - 1 < 4 and -5x - 3 < -3 is [tex]\left ( -\infty , 0 \right )[/tex].
What are equations and inequations?Algebraic expressions can be related to each other in many ways. When two expressions are equal to each other, they are called equations and are represented with an equal sign between them (=). When two expressions are not equal, they are called inequations and are represented by non-equal signs between them (>, <, ≥, ≤).
How to solve the given question?In the question, we are asked to solve the given inequations:
2x - 1 < 4 ... (i), and -5x -3 > -3 ... (ii).
First, we will solve (i), in the following ways:
2x - 1 < 4.
or, 2x - 1 + 1 < 4 + 1 (Adding 1 to both sides of the inequation)
or, 2x < 5 (Simplifying)
or, 2x/2 < 5/2 (Dividing both sides of the inequation by 2)
or, x < 5/2 (Simplifying)
or, x ∈ [tex]\left ( -\infty , \frac{5}{2} \right )[/tex] ...(iii)
Now, we will solve (ii), in the following ways:
-5x -3 > -3.
or, -5x - 3 + 3 > -3 + 3 (Adding 3 to both sides of the inequation)
or, -5x > 0 (Simplifying)
or, -5x/(-5) < 0/(-5) (Dividing both sides of the inequation by -5, sign of the inequality reverses as we are dividing by a negative number)
or, x < 0 (Simplifying)
or, x ∈ [tex]\left ( -\infty , 0 \right )[/tex] ...(iv)
For the solution set, we need the intersection of (iii) and (iv)
[tex]\left ( -\infty , \frac{5}{2} \right )[/tex] ∩ [tex]\left ( -\infty , 0 \right )[/tex]
= [tex]\left ( -\infty , 0 \right )[/tex]
∴ The solution set of the given set of linear inequations 2x - 1 < 4 and -5x - 3 < -3 is [tex]\left ( -\infty , 0 \right )[/tex].
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1. Round off each of the following to the nearest whole number.
(a) 8.71
(b) 26.01
(c) 69.48
(d) 103.72
(e) 49.84
(f) 101.35
(g) 39.814
(h) 1.23
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Hi there!
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[tex]8.71 = 9[/tex]
[tex]26.01 = 26[/tex]
[tex]69.48 = 69[/tex]
[tex]103.72 = 104\\49.84 = 50\\101.35 = 101\\39.814 = 40\\1.23 = 1[/tex]
❀Hope this helped you!❀
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Answer:
Step-by-step explanation:
Look at tenth place. If it is 5 , 6 ,7 , 8, 9 ( 5 or more than 5)then add 1 to the whole part and that is your answer
If it is 0,1,2,3,4, then write the whole number as it it.
a) 8.71
tenth place is 7 and it is more than 5. so, add 1 to the whole part. 8+1 = 9
8.71 = 9
b) 26.01
Tenth place is 0 and it is less than 5.So, write the whole number as it is.
26.01 = 26
c) 69.48 = 69 { 4 is less than 5}
d) 103.72 = 104 { 7 >= 5}
e) 49.84 = 50 { 8 >= 5}
f)101.35 = 101
g) 39.814 = 40
h)1.23 = 1
Joyce saved $130 on an item that was 35 % off. What was the original price?
Answer:
x=$200
Step-by-step explanation:
cross-multiply
130=0.65x
andrea is three times older than eliza. suzie is 4 years older then eliza. if eliza's age can be represented by x, create an expression that represents the combined age of all three girls
Answer:
Combined age = 5x+4 years
Step-by-step explanation:
let Eliza's age be x
given that Andrea is three times older than Eliza, hence Andrea's age is
= 3x years
it is also given that Suzie is 4 years older than eliza, hence Suzie's age is
= (x + 4) years
Therefore the combined age
= Eliza's age + Andrea's age + Suzie's age
= x + 3x + (x+4)
= x + 3x + x + 4
= 5x + 4
Find the slope of the line passing through the points (8, 3) and (9, 7)
Answer:
4
Step-by-step explanation:
Since we have 2 points, we can find the slope using
m = ( y2-y1)/(x2-x1)
= ( 7-3)/(9-8)
= 4/1
= 4
(8, 3) and (9, 7)
To Find:The slope of the line passing through the points (8, 3) and (9, 7).
Slope Formula:y2 - y1 / x2 - x1
Solution:7 - 3 / 9 - 8
= 4 / 1
= 4
Answer:4
adfh9qgfW9PGFgfogfwgr0fgwpORGFOAWGRO7GTFWARF
Answer:
sgjajzbjsjshissnbsjakskdksoddj XD
Step-by-step explanation:
Solve for g.
4(g - 17) = 12
g=
Answer:
[tex]g=20[/tex]
Step-by-step explanation:
[tex]4\left(g-17\right)=12[/tex]
Divide both sides by 4:
[tex]\frac{4\left(g-17\right)}{4}=\frac{12}{4}[/tex]
[tex]g-17=3[/tex]
Add 17 to both sides:
[tex]g-17+17=3+17[/tex]
[tex]g=20[/tex]
Answer: g=0 or g=20 i hope this helped
If the temperature in Texas dropped 35 degrees in 7 hours on Tuesday. What is the change over time?
Answer:
5 degrees every hour.
Step-by-step explanation:
35/7=5
Answer: 5
Step-by-step explanation:
35 degrees / 7 hours = 5 degrees per hour
8 1/3 in 10 minutes
find unit rate
Inverse functions, PLEASE HELP I’m stuck
Place the numbers in order from least to greatest.
0.24,4 x 10^-2,0.042, 2 x 10^-4,0.004
Answer:
2x10^-4,0.004,4x10^-2,,0.042,0.24
Step-by-step explanation:
i did the paper
If 9% of a number equals 5, find 36% of that number.
Answer:
20
Step-by-step explanation:
You can set this up in an algebraic equation:.09x=5 which translates to 9% times a variable or unknown number equals 5Divide both sides by .09 which turns to 55.5 Multiply by .36 to find 36% of that number which equals 20What are two different methods you can use to withdraw money from your checking account?
Answer:
You can withdraw by automatic electronic transfer, check, ATM card or debit card. There are many ways these days to withdraw money from your accounts.Use the digits 1-5 to make the smallest whole number possible. Write your answer in standard, expanded, and word form.
Answer:
1 in standard form, 1 in expanded form, and one in word form.
Step-by-step explanation:
Hope this helps! If it does, please mark me brainliest! Thank you! ;)
Elena draws a scale drawing for a garden in her backyard. The scale drawing is 3 inches by 6 inches. The garden will be 12 feet by 24 feet. What is the scale of the drawing in inches to feet? IF YOU ANSWER THIS QUESTION RIGHT I WILL MARK YOU BRAINLIEST 50 POINT QUESTION
plzzz give brainliest i really need it for my next rank
Answer:
1 inch= 4 feet for both
Step-by-step explanation:
This also means that the scale converts to 1/4 in. = 12 in.
stay safe
Using proportions, it is found that the scale is of 0.25 inches per feet.
This question is solved by proportions, using a rule of three.3 inches represents 12 feet, while 6 inches represents 24 feet. Since they are multiples, we take one of them, and find how many inches are represented by 1 feet.The rule of three is:
3 inches - 12 feet
x inches - 1 feet
Applying cross multiplication:
[tex]12x = 3[/tex]
[tex]x = \frac{3}{12}[/tex]
[tex]x = \frac{1}{4}[/tex]
[tex]x = 0.25[/tex]
The scale is of 0.25 inches per feet.
To learn more about proportions, you can check https://brainly.com/question/24372153
There are 4 consecutive integers that have a sum of 34. What are the integers
Answer:
consider integer are x, x+1, x+2, x+3
now x+(x+1) + (x+2) + (x+3) = 34
or, 4x + 6 = 34
or, 4x =28
x= 7
x =7
x+1 = 7+1 =8
x+2= 7+2=9
x+3= 7+3 =10
Answer:
Step-by-step explanation: 7,8,9,10
What’s the answer confused with this ??
Answer:
x = - 1
option I
Step-by-step explanation:
Equation is: 5x + 6 = 1
Subtract 6 from both sides
5x + 6 - 6 = 1 -6
5x = -5
Divide both sides by 5
5x / 5 = -5/5
x = -1
What am I doing wrong in step 5?
Step-by-step explanation:
t = 9x, and dx = 1/9 dt.
∫ sin(9x) dx
= ∫ sin(t) (1/9 dt)
= 1/9 ∫ sin(t) dt
= -1/9 cos(t)
= -1/9 cos(9x)
A speedboat moves at a rate of 25 km/hr in still water. How long will it take
someone to ride the boat 87 km downstream if the river's current moves at a rate of
4 km/hr?
3 hours
I hope this helps you
Which table of ordered pairs represents a proportional relationship?
Answer:
2nd one
For example 5 squared is 25, 7 Squared is 49, and 9 Squared is 81
The larger of two numbers is four more than the smaller. If the larger is x, what is the smaller?
Answer:
Step-by-step explanation:
x is the larger. The smaller is 4 less than the larger
x - 4 would be the smaller.
Answer:
x-4 is the smaller
Marissa drives from her house to work at an avg speed of 40mph. She drives home sameroute at 60mph. Entire round trip is 45 minutes, what is her avgspeed in mph?
Answer:
50mph
Step-by-step explanation:
to to find the mean you add 40 + 60. which equals 100 then divide by the amount a variables which is two.
what is a median of 11,16,29,29,29,33,52,52,52
Tula can paint 2/3 of a room in 3/4 hours. How many rooms can she paint in one hour?
Answer:
She can paint 1 1/2 of a room
Step-by-step explanation:
I believe...
Answer:
8/9
its just simple equations
you do 2/3 divided by 3/4 for the unit rate.
If $8500 is invested at 3.4% interest, compounded monthly, how much will the
investment be worth in 23 years?
O A. $18,339.66
O B. $9,071.53
O C. $19,142.10
O D. $18,559.10
Answer:
In 23 years, you will have $18,559.10
Step-by-step explanation:
Pablo's retirement party will cost $8 if he invites 4 guests. If there are 6 guests, how
will Pablo's retirement party cost? Solve using unit rates.
Answer:
$12
Step-by-step explanation:
Step 1:
$8 : 4 = x : 6
Step 2:
4x = 48
Answer:
x = 12
Hope This Helps :)
Whats the answer for −2 1/2,−5 3/4 The distance between the two numbers is
Answer:
3 1/4
Step-by-step explanation:
-5 3/4 + 3 1/4 = -2 1/2
The probability that an event will happen is P(E)=
34/41.
Find the probability that the event will not happen.
Answer:
7/41
Step-by-step explanation:
There is a 34/41 probability that this event will happen so to find the probability of which the event will not happen, the subtract 34 from 41 to get your answer.
41-34=7
Therefore, 7/41 is the answer.
Ps. is the P(E) included in the main question? if it is, the the answer might differ from the one I am giving you.
What standard measurement would be best used to determine how much milk is in a milk carton for lunch?
A coin was tossed 60 times and the coin landed on Heads 35 times. What proportion of the time did the coin land on Heads?
Type your numeric answer and submit
Answer:
35:60 times
Step-by-step explanation:
The proportion of time in which the coin land on Heads is 0.58
What is proportion?A proportion is an equation in which two ratios are set equal to each other.
Now it is given that,
Number of times coins tossed = 60
Number of times coin landed on Heads = 35
Therefore, the proportion of time in which the coin land on Heads is given as,
Proportion of time the coin land on Heads = Number of times coin landed on Heads/Number of times coins tossed
⇒ Proportion of time the coin land on Heads = 35/60
⇒ Proportion of time the coin land on Heads = 7/12 = 0.58
Thus, the proportion of time in which the coin land on Heads is 0.58
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Solve the following inequality 90 > 10x + 80
Answer:
x<1
Step-by-step explanation:
10x + 80 < 90
10x < 90 - 80
10x < 10
x < 1