Question

sometimes, it can be helpful to rewrite part of an equation by using the distributive property or combining like terms. consider the equation below with that in mind. what is the value of x?
subtract 6x from both sides, then rewrite the equation to represent the remaining values.
18x + 24 = 6(x - 4)
18x + 24 = 6x - 24

• 6x - 6x

□ = □

Explanation:

Step1: Subtract 6x from left side

Left side: \(18x + 24 - 6x = (18x - 6x)+24 = 12x + 24\)

Step2: Subtract 6x from right side

Right side: \(6x - 24 - 6x = (6x - 6x)-24 = -24\)
Wait, but actually, after subtracting 6x from both sides, we have:
Left side: \(18x + 24 - 6x = 12x + 24\)
Right side: \(6x - 24 - 6x = -24\)
But maybe the problem is first to fill the blanks after subtracting 6x, then solve for x. Wait, let's redo:

Original equation after expanding: \(18x + 24 = 6x - 24\)
Subtract 6x from both sides:
Left: \(18x - 6x + 24 = 12x + 24\)
Right: \(6x - 6x - 24 = -24\)
So the blanks are \(12x + 24\) and \(-24\). Then to solve for x, we can continue:
Subtract 24 from both sides: \(12x + 24 - 24 = -24 - 24\)
\(12x = -48\)
Divide by 12: \(x = -4\)
But the first part is filling the blanks after subtracting 6x. So the left blank is \(12x + 24\), right blank is \(-24\). Then solving for x gives x = -4.

Wait, the problem says "Subtract 6x from both sides, then rewrite the equation to represent the remaining values." So first, do the subtraction:

Left side: \(18x + 24 - 6x = 12x + 24\)
Right side: \(6x - 24 - 6x = -24\)
So the equation becomes \(12x + 24 = -24\)
Then, to solve for x:

Step3: Subtract 24 from both sides

\(12x + 24 - 24 = -24 - 24\)
\(12x = -48\)

Step4: Divide by 12

\(x = \frac{-48}{12} = -4\)

Answer:

The value of \(x\) is \(-4\). And the blanks after subtracting 6x are \(12x + 24\) and \(-24\).