Consider this equation:
4(3x−2)=−24
Part 1. What is your first step in solving this equation? Remember, there is more than one way to solve this equation.
Part 2. How would you isolate the variable and solve for x after you have completed Part 1?
You do not need to solve the problem. Simply, describe your process.
**Please label Part 1 and Part 2 in your answer.**
(2 points)
Part 1: The first step in solving this equation is to distribute the 4 to the terms inside the parentheses. This can be done by multiplying 4 with both 3x and -2.
Part 2: After distributing the 4, the equation will become 12x - 8 = -24. To isolate the variable x, we can start by adding 8 to both sides of the equation to get rid of the constant term on the left side. This gives us 12x = -16. Finally, we can divide both sides of the equation by 12 to solve for x.
This process involves applying the distributive property and performing addition and division operations to isolate and solve for the variable x.
Part 1:
To solve the equation 4(3x - 2) = -24, the first step would be to simplify the expression on the left side of the equation. We can do this by applying the distributive property, which means multiplying each term inside the parentheses by the number outside the parentheses.
So, we would start by multiplying 4 with each term inside the parentheses:
4 * 3x = 12x
4 * -2 = -8
After applying the distributive property, the equation becomes:
12x - 8 = -24
Part 2:
To isolate the variable x and solve for it, we need to get rid of the constant term (-8) on the left side of the equation. We can do this by performing the inverse operation, which is adding 8 to both sides of the equation:
12x - 8 + 8 = -24 + 8
Simplifying further:
12x = -16
Finally, to solve for x, we divide both sides of the equation by the coefficient of x (12 in this case):
12x/12 = -16/12
Simplifying the division:
x = -4/3
Therefore, the value of x that satisfies the equation 4(3x - 2) = -24 is x = -4/3.