Question

Is x = 6 a solution to the equation 5(x – 3) = x + 13? Follow the steps to find out.

1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true.


2. Simplify both sides. Show your work.


3. Is x = 6 a solution to the equation? Why or why not?


4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)

Answer 1

First you substitute 6 for x!

5(6 - 3) = 6 + 13

6 - 3 = 3

The equation is now:

5 * 3 = 6 + 13

5 * 3 = 15

6 + 13 = 19

The result is:

15 = 19 which is not a true statement.

x is not equal to 6.

Now lets try 7.

5(7 - 3) = 7 + 13

7 - 3 = 4

7 + 13 = 20

5 * 4 = 20

Thus: x = 7

Explanation:

Hope it helps! =D

Answer 2

see below

Explanation:

Step 1

5(x – 3) = x + 13

Step 2

See if x is a solution

5 (6-3) ?= 6+13

5 (3) ?= 19

15 ?= 19

Step 3

This is not true so it is not a solution

Step 4

5(x – 3) = x + 13

Distribute

5x-15 = x+3

Subtract x from each side

5x-x -15 = x+13-x

4x-15 = 13

Add 15 to each side

4x-13+13 = 15+13

4x =28

Divide each side by 4

4x/4 = 28/4

x = 7

7 is a solution