Question

what does $4(x + 2)$ represent?
4 groups of $x + 2$
how can you isolate the expression $x + 2$
? 4 on both sides.
$4(x + 2) = 12$

Explanation:

To isolate \( x + 2 \) in the equation \( 4(x + 2)=12 \), we use the inverse operation of multiplication, which is division. We divide both sides of the equation by 4.

Step 1: Divide both sides by 4

The equation is \( 4(x + 2)=12 \). To isolate \( x + 2 \), we divide both sides by 4. Mathematically, this is:
\[
\frac{4(x + 2)}{4}=\frac{12}{4}
\]

Step 2: Simplify both sides

Simplifying the left - hand side, the 4 in the numerator and denominator cancels out, leaving \( x + 2 \). For the right - hand side, \( \frac{12}{4}=3 \). So we get:
\[
x + 2 = 3
\]

So the operation to isolate \( x + 2 \) from \( 4(x + 2)=12 \) is to divide both sides by 4.

If we were to answer the fill - in - the - blank (the dropdown question "how can you isolate the expression \( x + 2 \)? [dropdown] 4 on both sides"), the operation is "Divide" (because we divide both sides by 4 to isolate \( x+2\) from \( 4(x + 2)\)).

For solving \( 4(x + 2)=12 \) for \( x\):

Step 1: Isolate \( x + 2\)

As above, divide both sides by 4:
\[
\frac{4(x + 2)}{4}=\frac{12}{4}\implies x + 2=3
\]

Step 2: Isolate \( x\)

Subtract 2 from both sides of the equation \( x + 2=3\):
\[
x+2 - 2=3 - 2\implies x = 1
\]

But focusing on isolating \( x + 2\), the key operation is dividing both sides by 4.

Answer:

To isolate \( x + 2 \) in the equation \( 4(x + 2)=12 \), we use the inverse operation of multiplication, which is division. We divide both sides of the equation by 4.

Step 1: Divide both sides by 4

The equation is \( 4(x + 2)=12 \). To isolate \( x + 2 \), we divide both sides by 4. Mathematically, this is:
\[
\frac{4(x + 2)}{4}=\frac{12}{4}
\]

Step 2: Simplify both sides

Simplifying the left - hand side, the 4 in the numerator and denominator cancels out, leaving \( x + 2 \). For the right - hand side, \( \frac{12}{4}=3 \). So we get:
\[
x + 2 = 3
\]

So the operation to isolate \( x + 2 \) from \( 4(x + 2)=12 \) is to divide both sides by 4.

If we were to answer the fill - in - the - blank (the dropdown question "how can you isolate the expression \( x + 2 \)? [dropdown] 4 on both sides"), the operation is "Divide" (because we divide both sides by 4 to isolate \( x+2\) from \( 4(x + 2)\)).

For solving \( 4(x + 2)=12 \) for \( x\):

Step 1: Isolate \( x + 2\)

As above, divide both sides by 4:
\[
\frac{4(x + 2)}{4}=\frac{12}{4}\implies x + 2=3
\]

Step 2: Isolate \( x\)

Subtract 2 from both sides of the equation \( x + 2=3\):
\[
x+2 - 2=3 - 2\implies x = 1
\]

But focusing on isolating \( x + 2\), the key operation is dividing both sides by 4.