Quiz 1 problem 10

10. Solve for x and check.

2(3x + 5) - (x - 3) = 2x - 6

First remove parentheses

6x + 10 - x + 3 = 2x - 6

Now combine like terms

5x + 13 = 2x - 6

Transpose known terms to one side and unknown terms to the other

side.

5x - 2x = -13 - 6

3x = -19

x = -19/3

Check

2(3(-19/3) + 5) - ((-19/3) - 3) = 2(-19/3) - 6

Inside the first parentheses, 3(-19/3) = -19

2(-19 + 5) - ((-19/3) - 3) = 2(-19/3) - 6

Inside the second parentheses we are subtracting fractions. We can

handle this situation by finding common denominators. 3 = 9/3.

2(-19 + 5) - ((-19/3) - 9/3) = 2(-19/3) - 6

2(-19 + 5) - (-28/3) = 2(-19/3) - 6

On the left, subtracting a negative is the same as adding a positive,

and on the right, 2(19/3) = 38/3

2(-19 + 5) + 28/3 = -38/3 - 6

Inside the parentheses that are still on the left, -19 + 5 = -14

2(-14) + 28/3 = -38/3 - 6

Multiply the 2(-14)

-28 + 28/3 = -38/3 - 6

Find common denominators.

-84/3 + 28/3 = -38/3 - 18/3

-56/3 = -56/3