Question3. What value of $x$ makes the following equation true? $-6(x-4)=60$

Studdy Solution

STEP 1

What is this asking? Find the number that makes the equation $-6(x-4)=60$ true. Watch out! Don't forget to distribute the $-6$ to both terms inside the parentheses!

STEP 2

1. Distribute the $-6$
2. Simplify the equation
3. Solve for $x$

STEP 3

Alright, let's distribute the $-6$ across the terms inside the parentheses.
This means we'll multiply $-6$ by both $x$ and $-4$ .
$-6(x - 4) = -6 \cdot x + (-6) \cdot (-4)$

STEP 4

Calculate each part:
- $-6 \cdot x = -6x$ - $(-6) \cdot (-4) = 24$
So, the equation becomes:
$-6x + 24 = 60$

STEP 5

Now let's simplify the equation by getting rid of the $24$ on the left side.
We'll subtract $24$ from both sides to keep the equation balanced:
$-6x + 24 - 24 = 60 - 24$

STEP 6

This simplifies to:
$-6x = 36$

STEP 7

To solve for $x$ , we need to divide both sides by $-6$ to get $x$ by itself.
Remember, dividing by $-6$ is like finding out how many times $-6$ fits into $36$ .
$x = \frac{36}{-6}$

STEP 8

Calculate the division:
$x = -6$

STEP 9

The value of $x$ that makes the equation true is $\mathbf{-6}$ .

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