Question

3.
-3x - 6(2.5x + 33) - 12 = 12x
x = 70 \t x = 7 \t x = -7
black \t brown \t dark green

Explanation:

Step1: Expand the bracket

First, we expand \(-6(2.5x + 33)\) using the distributive property \(a(b + c)=ab+ac\). So, \(-6\times2.5x=-15x\) and \(-6\times33 = - 198\). The equation becomes \(-3x-15x - 198-12=12x\).

Step2: Combine like terms

Combine the \(x\)-terms on the left: \(-3x-15x=-18x\), and the constant terms: \(-198 - 12=-210\). Now the equation is \(-18x-210 = 12x\).

Step3: Move \(x\)-terms to one side

Add \(18x\) to both sides to get all \(x\)-terms on the right: \(-210=12x + 18x\).

Step4: Combine \(x\)-terms on the right

\(12x+18x = 30x\), so the equation is \(-210 = 30x\).

Step5: Solve for \(x\)

Divide both sides by 30: \(x=\frac{-210}{30}=-7\).

Answer:

\(x = - 7\) (corresponding to dark green)