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PGCPS Math 8 - Summer 2024

### Checking Your Understanding

Follow the steps to solve this equation:
[tex]\[ -2x + 6x - 8 = 12 \][/tex]

Step 1: Combine like terms.

[tex]\[
\begin{aligned}
4x - 8 &= 12 \\
4x - 8 + 8 &= 12 + 8 \\
4x &= 20 \\
\frac{4x}{4} &= \frac{20}{4} \\
x &= 5
\end{aligned}
\][/tex]

Step 2: Undo the multiplication.

(Note: There was an error in the original solution; the corrected value of [tex]\( x \)[/tex] is 5.)

Sagot :

GinnyAnsweridn
Let's carefully solve the equation [tex]\( -2x + 6x - 8 = 12 \)[/tex] step-by-step.

### Step 1: Combine like terms
First, combine the terms that contain [tex]\( x \)[/tex]:

[tex]\[ -2x + 6x - 8 = 12 \][/tex]

Combine [tex]\( -2x \)[/tex] and [tex]\( 6x \)[/tex]:

[tex]\[ (6x - 2x) - 8 = 12 \][/tex]

This simplifies to:

[tex]\[ 4x - 8 = 12 \][/tex]

### Step 2: Isolate the term with [tex]\( x \)[/tex]
To isolate the term with [tex]\( x \)[/tex], add 8 to both sides of the equation:

[tex]\[ 4x - 8 + 8 = 12 + 8 \][/tex]

This simplifies to:

[tex]\[ 4x = 20 \][/tex]

### Step 3: Solve for [tex]\( x \)[/tex]
To solve for [tex]\( x \)[/tex], divide both sides of the equation by 4:

[tex]\[ \frac{4x}{4} = \frac{20}{4} \][/tex]

This simplifies to:

[tex]\[ x = 5 \][/tex]

So, the solution to the equation [tex]\( -2x + 6x - 8 = 12 \)[/tex] is [tex]\( x = 5 \)[/tex].
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