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

First, we expand the left - hand side and the right - hand side of the equation \(1.5(x + 4)-3=4.5(x - 2)\).
For the left - hand side:
Using the distributive property \(a(b + c)=ab+ac\), where \(a = 1.5\), \(b=x\) and \(c = 4\), we have \(1.5(x + 4)=1.5x+1.5\times4=1.5x + 6\). Then subtract 3: \(1.5x+6 - 3=1.5x+3\).
For the right - hand side:
Using the distributive property \(a(b - c)=ab - ac\), where \(a = 4.5\), \(b=x\) and \(c = 2\), we get \(4.5(x - 2)=4.5x-4.5\times2=4.5x - 9\).
So the equation becomes \(1.5x+3=4.5x - 9\).

Step2: Move the terms with x to one side

Subtract \(1.5x\) from both sides of the equation \(1.5x+3=4.5x - 9\).
\(1.5x+3-1.5x=4.5x - 9-1.5x\)
Simplifying both sides, we have \(3 = 3x-9\).

Step3: Solve for x

Add 9 to both sides of the equation \(3 = 3x-9\).
\(3 + 9=3x-9 + 9\)
\(12=3x\)
Then divide both sides by 3: \(\frac{12}{3}=\frac{3x}{3}\), so \(x = 4\).

Answer:

4