Question

how many solutions exist for the given equation?
$3(x - 2) = 22 - x$
zero
one
two
infinitely many

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b - c)=ab - ac\), we expand \(3(x - 2)\) to get \(3x-6\). So the equation becomes \(3x - 6=22 - x\).

Step2: Add \(x\) to both sides

Adding \(x\) to both sides of the equation \(3x - 6=22 - x\) gives \(3x+x - 6=22 - x+x\), which simplifies to \(4x - 6=22\).

Step3: Add 6 to both sides

Adding 6 to both sides of \(4x - 6=22\) gives \(4x-6 + 6=22 + 6\), so \(4x=28\).

Step4: Divide by 4

Dividing both sides of \(4x = 28\) by 4 gives \(x=\frac{28}{4}=7\). Since we found a unique solution for \(x\), the equation has one solution.

Answer:

one