Question

what value of ( x ) makes the equation true?( 3(x + 4) = 2x - 6 )a. ( -18 )b. ( 18 )c. ( -6 )d. ( 6 )a( circ )b( circ )c( circ )d( circ )

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(3(x + 4)\) to get \(3x+12\). So the equation becomes \(3x + 12=2x-6\).

Step2: Subtract \(2x\) from both sides

Subtracting \(2x\) from both sides of the equation \(3x + 12=2x-6\) gives \(3x-2x+12=2x - 2x-6\), which simplifies to \(x + 12=-6\).

Step3: Subtract 12 from both sides

Subtracting 12 from both sides of \(x + 12=-6\) gives \(x+12 - 12=-6-12\), so \(x=-18\). Wait, no, wait, let's check again. Wait, step 2: \(3x+12 = 2x - 6\), subtract \(2x\) from both sides: \(x + 12=-6\), then subtract 12: \(x=-6 - 12=-18\)? Wait, but let's plug back in. If \(x=-18\), left side: \(3(-18 + 4)=3(-14)=-42\), right side: \(2(-18)-6=-36 - 6=-42\). Oh, right, so my initial calculation was correct. Wait, but let's do the steps again carefully.

Wait, original equation: \(3(x + 4)=2x-6\)

Step 1: Distribute 3: \(3x+12 = 2x-6\)

Step 2: Subtract \(2x\) from both sides: \(3x-2x+12=2x-2x - 6\) => \(x + 12=-6\)

Step 3: Subtract 12 from both sides: \(x=-6 - 12=-18\)

Yes, so \(x=-18\), which is option A.

Wait, but let's check the options. Option A is -18, so that's correct.

Answer:

A. \(-18\)