Question

Consider this equation:%0D%0A%0D%0A4(3x−2)=−24%0D%0A4%0D%0A(%0D%0A3%0D%0A%0D%0A−Part 1. What is your first step in solving this equation? Remember, there is more than one way to solve this equation.%0D%0A%0D%0APart 2. How would you isolate the variable and solve for x after you have completed Part 1?%0D%0A%0D%0AYou do not need to solve the problem. Simply, describe your process.

Answer 1

Part 1: The first step in solving this equation is to distribute the 4 to both terms inside the parentheses. This can be done by multiplying 4 with each term inside the parentheses:

4 * 3x = 12x
4 * (-2) = -8

The equation now becomes:
12x - 8 = -24

Part 2: To isolate the variable and solve for x, we need to get rid of the constant term (-8) on the left side of the equation. We can do this by adding 8 to both sides:

12x - 8 + 8 = -24 + 8
12x = -16

Finally, to solve for x, we divide both sides of the equation by 12:

12x/12 = -16/12
x = -4/3

So, the process involves distributing the 4, combining like terms, isolating the variable by getting rid of the constant term, and then solving for x.