Question

what is the value of x in the equation $1.5(x + 4) - 3 = 4.5(x - 2)$?
4
3
9
5

Explanation:

Step1: Expand both sides

Expand \(1.5(x + 4)-3\) and \(4.5(x - 2)\) using the distributive property \(a(b + c)=ab+ac\).
For the left - hand side:
\(1.5(x + 4)-3=1.5x+1.5\times4 - 3=1.5x + 6-3=1.5x+3\)
For the right - hand side:
\(4.5(x - 2)=4.5x-4.5\times2=4.5x - 9\)
So the equation becomes \(1.5x + 3=4.5x-9\)

Step2: Move the terms with x to one side and constants to the other

Subtract \(1.5x\) from both sides:
\(1.5x+3 - 1.5x=4.5x-9 - 1.5x\)
Simplify to get \(3 = 3x-9\)
Then add 9 to both sides:
\(3 + 9=3x-9 + 9\)
Simplify to get \(12 = 3x\)

Step3: Solve for x

Divide both sides of the equation \(12 = 3x\) by 3:
\(x=\frac{12}{3}=4\)

Answer:

4