Final answer:
To solve the equation 2(7x-2)-3(2x + 6) = 38, you start by distributing the numbers outside the parentheses, combine like terms, and isolate the variable x to find that x equals 7.5.
Step-by-step explanation:
We're solving the equation 2(7x-2)-3(2x + 6) = 38 for x.
First, distribute the numbers outside the parentheses:
- 2 × 7x = 14x
- 2 × (-2) = -4
- -3 × 2x = -6x
- -3 × 6 = -18
Combine these to get the equation:
14x - 4 - 6x - 18 = 38
Now, combine like terms:
14x - 6x = 8x
-4 - 18 = -22
So the simplified equation is:
8x - 22 = 38
Now add 22 to both sides to isolate the variable term:
8x - 22 + 22 = 38 + 22
Which simplifies to:
8x = 60
Finally, divide both sides by 8:
x = 60 / 8
x = 7.5