Question

solving linear equations: distributive prop quiz complete 1 2 3 4 5 6 what is the value of x in the equation ( 1.5(x + 4) - 3 = 4.5(x - 2) )?
3
4
5
9

Explanation:

Step1: Apply distributive property

First, apply the distributive property to both sides of the equation. For the left - hand side, distribute \(1.5\) to \((x + 4)\):
\(1.5(x + 4)=1.5x+1.5\times4 = 1.5x + 6\)
So the left - hand side of the equation \(1.5(x + 4)-3\) becomes \(1.5x+6 - 3=1.5x + 3\)

For the right - hand side, distribute \(4.5\) to \((x - 2)\):
\(4.5(x - 2)=4.5x-4.5\times2=4.5x - 9\)

Now our equation is \(1.5x+3 = 4.5x-9\)

Step2: Move like terms together

Subtract \(1.5x\) from both sides of the equation to get:
\(1.5x+3-1.5x=4.5x - 9-1.5x\)
\(3 = 3x-9\)

Then add \(9\) to both sides of the equation:
\(3 + 9=3x-9 + 9\)
\(12 = 3x\)

Step3: Solve for x

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

Answer:

\(4\) (corresponding to the option with value 4)