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

Explanation:

Step1: Expand the equation

Use the distributive property (a(b + c)=ab+ac). [ \begin{align*} 1.5(x + 4)-3&=4.5(x - 2)\ 1.5x+6 - 3&=4.5x-9\ 1.5x + 3&=4.5x-9 \end{align*} ]

Step2: Move the terms with (x) to one side

Subtract (1.5x) from both sides. [ \begin{align*} 1.5x+3-1.5x&=4.5x - 9-1.5x\ 3&=3x-9 \end{align*} ]

Step3: Isolate the term with (x)

Add (9) to both sides. [ \begin{align*} 3 + 9&=3x-9+9\ 12&=3x \end{align*} ]

Step4: Solve for (x)

Divide both sides by (3). [x=\frac{12}{3}=4]

Answer:

(4)