Find the value of a for which the solution of the inequality is all real numbers

a(x + 3) < 5x + 15 - X

Answer:

x = 3

Step-by-step explanation:

 (3 • (5x - 15)) -  15 • (x - 3)  = 0  

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  5x - 15  =   5 • (x - 3)  

Equation at the end of step

3

:

 15 • (x - 3) -  15 • (x - 3)  = 0  

STEP

4

:

Pulling out like terms

4.1      Pull out     15  

Pulling out like terms :

4.2      Pull out     x-3  

After pulling out, we are left with :

     15 • x-3 • ( 1  *  1 +( (-1)  *  (-1) ))

Equation at the end of step

4

:

 30 • (x - 3)  = 0  

STEP

5

:

Equations which are never true

5.1      Solve :    30   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.2      Solve  :    x-3 = 0  

Add  3  to both sides of the equation :  

                     x = 3

One solution was found :

x = 3

The required value of a for which the solution of the inequality is all real numbers is a > 4.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now the given inequality is,

a(x + 3) < 5x + 15 - x

or, a(x + 3) < 4x + 15

Now let us solve for x first,

⇒ ax + 3a  < 4x + 15

Subtract 3a from both sides we get,

ax < 4x + 15 - 3a

Subtract 4x from both sides we get,

ax - 4x < 15 - 3a

or, (a - 4)x < 15 - 3a

Dividing both the side by (a - 4) we get,

x < (15 - 3a) / (a - 4)

Now for solutions to be real numbers,

a - 4 > 0

subtracting 4 both the side we get,

⇒ a > 4

this is the required value of a for which the solution of the inequality is all real numbers

Thus, the required value of a for which the solution of the inequality is all real numbers is a > 4.

To learn more about inequality :

https://brainly.com/question/13363104

#SPJ2

Patulong naman sa business math HAHHA

How do i simplify the expression 6(x+2)-4

What is the equation of the vertical line through -8, 5

how do you do this ??​

find the difference
5/6-7/10​

The water level at Lake Livingston last week was 3.45 inches below sea level. After a heavy rain, the lake measured 2.9 inches above sea level. What was the change in the water level?

Please help me please I feel like crying cause I can't do it...

can Yhu help me plzzz!!!!
​

What is 4÷97 answered as a decimal?

Both questions in picture! Will give brainliest!!

Someone plz answer

the school jimmy goes to is selling tickets to a fall musical. om the first day of ticket sales the school sold 9 adult tickets and 14 child tickets for $101. The school took in $88 on the second day by selling 12 adult tickets and 7 critical tickets. What is the price each of one adult ticket and one child ticket.

ASAP WILL GOVE BRAINLIEST FO YOU EXPLAIN AND GIVE ME ANSWER ASAP

Easy 7th grade work sheet ! Please help , I’ll give brainliest (all answers)

answerrrr plssssssssssssssssssssssssssssssssssss

What is the area of the triangle?

James has $40 to spend. He wants to buy 2 tickets to a show. He has to spend $7 to get where tickets are sold. The following inequality can be used to find out the highest price James can afford to pay for each ticket. 2x+7 less than or equal to 40.
A.) x less than or equal to 23.5
B.) x less than or equal to 16.5
C.) x greater than or equal to 23.5
D.) x greater than or equal to 16.5

A shop sells bagels for $5 per dozen. You can use the table to answer
the questions. Explain your reasoning. (Show all your work)

1. At this rate, how much would 6 bagels cost?

2. How many bagels can you buy for $50?

Which of the following statements does not represent the same value as the others?

the distance between 0 and −9
the absolute value of negative 9
the opposite of 9
the absolute value of 9

What is the equation of the line that passes through the point (1,0) and has a slope
of 1?

14:6 divided by 5 ( the 14:6 is a ration )

-0.6 repeating terminating or neither

I WILL GIVE BRAINLIEST AND 36 Points
Refer to screenshots

8. Which line on the graph represents the equation y=3x-2?
line A
line B
line C
line D

9.Which equation represents the graph?

y = |x| – 4

y = |x – 4|

y = |x + 4|

y = |x| + 4

12.Which equation represents the graph?

y = |x| + 6

y = |x – 6|

y = |x| – 6

y = |x + 6|

17.Which set of ordered pairs corresponds to the graph?

{(5, 1), (4, 2), (0, –1), (–2, 3), (–5, 1)}

{(–2, 3), (5, 1), (–5, 1), (1, 0), (4, –2)}

{(–5, –1), (–2, 3), (0, –1), (4, –2), (5, 1)}

{(–2, 4), (–1, –5), (–1, 0), (1, 5), (3, –2)}

19.Which equation is represented by the table?
Y=-|X-1|-4
Y=|X-1|-4
Y=-|X+1|-4
Y=|X+1|-4

Jason had one hundred fifty-nine dollars to spend six books.After buying them he had fifteen dollars.How much did each book cost.

y=-3x-1 find slope and y interceapt

If Mariana scores 5 points how many points did aki score

Are any of these numbers an Integer?
15
20/5
44
13/19
-35.47
;w; help

Hello pls helppppppppppp

Car Y travels 105 miles on 3 gallons of petrol. Car Z travels 80 miles on 9 litres of petrol.

Which car has better petrol consumption ( more miles per gallon)?

You may use the fact that 1 gallon =4.5 litres


Options are

A. None

B. Y

C. Z

please answer this I really need help if you just take my points ill report I just need help pleassesssseessesesee!!!!!!!! (15 points!)

How many solutions does the following equation have? -6(x + 7) = -42 - 2​