Question

Given the equation 4x + 7 = 3(2x − 5), solve for the variable. Explain each step and justify your process. Sam solved a similar equation below. Is Sam's solution correct? Explain why or why not. 5x − 1 = 2(x + 4) 5x − 1 = 2x + 8 7x − 1 = 8 7x = 7 x = 1

Answer 1

to solve the first part

- distribute the 3 to the 2x and the -5

- the equation will now read 4x-7=6x-15

-subtract 7 from both sides
4x=6x-22
- subtract 6x from both sides
-2x=-22
-divide both sides by -2
x=11

the second part- sam is wrong because x should equal 3
-distribute 2 to the x and the 4
5x-1=2x+8
-subtract 2x from each side
3x-1=8
-add 1 to each side
3x=9
-divide each side by 3
x=3

Answer 2

4x + 7 = 3(2x - 5)

MY SOLUTION :

Simplify the right side of the equation.

4x + 7 = 6x - 15

We're essentially trying to get "x" by itself so that we could solve for it.

So, simply subtract 6x from both sides, as well as subtracting 7 from both sides.

4x - 6x = - 15 - 7

Simplify.

-2x = -22

Divide both sides by -2.

x = 11

SAM'S SOLUTION :

5x - 1 = 2(x + 4)

Step 1) 5x - 1 = 2x + 8

Step 2) 7x - 1 = 8

Step 3) 7x = 7

Step 4) x = 1

Sam messed up in Step 2, because when moving a positive to the other side of an equal sign, you must turn it into negative. Due to the fact that Sam kept it as a positive, he messed up.

~Hope I helped!~