Question

For what value of x does 4(3x - 2) = 12?
a. 2/3
b. 24
c. 1
d. 5/3

Answer 1

To solve the equation 4(3x - 2) = 12, we distribute the 4, combine like terms, and then divide by 12 to isolate x, resulting in x = 5/3 as the solution.

Step-by-step explanation:

To find the value of x for which 4(3x - 2) = 12, we need to follow a series of algebraic steps to isolate x:

1. First, distribute the 4 into the parentheses: 4 * 3x - 4 * 2 = 12x - 8.
2. Next, simplify the equation to its basic form, which in this case is already done.
3. Move all terms containing x to one side and constant terms to the opposite side.
4. Divide both sides by the coefficient of x, which is 12, to get x by itself.

Now let's solve the equation step-by-step:

1. 4(3x - 2) = 12
2. 12x - 8 = 12 (Distributive Property applied)
3. 12x = 12 + 8 (Add 8 to both sides)
4. 12x = 20 (Combine like terms)
5. x = 20 / 12 (Divide both sides by 12)
6. x = 5/3 (Simplify the fraction)

Therefore, the value of x for which 4(3x - 2) = 12 is 5/3.