Question

Solve 4x - 2(x + 1) = 3x + 10.
a. -12
b. 12
c. - 8
d. 8

Answer 1

The solution to the given linear equation 4x - 2(x + 1) = 3x + 10 is x = -12. By distributing, combining like terms, and isolating the variable, we find that the correct answer is option a.

Step-by-step explanation:

To solve the equation 4x - 2(x + 1) = 3x + 10, we start by expanding and simplifying the expressions on both sides. First, we distribute the -2 across the parentheses on the left side:

• 4x - 2*x - 2*1 = 3x + 10
• 4x - 2x - 2 = 3x + 10

Next, we combine like terms on the left side:

• (4x - 2x) - 2 = 3x + 10
• 2x - 2 = 3x + 10

Then, we subtract 3x from both sides to get all the x terms on one side:

• 2x - 3x - 2 = 3x - 3x + 10
• -x - 2 = 10

Now, we add 2 to both sides to isolate the x:

• -x - 2 + 2 = 10 + 2
• -x = 12

To find the value of x, we divide both sides by -1:

• -x / -1 = 12 / -1
• x = -12

Thus, the solution to the equation is x = -12, which corresponds to option a.