Question

solve for x. -6(3x - 2) + 4x = -4(x + 1)

Explanation:

Step1: Expand both sides

First, we expand the left - hand side and the right - hand side of the equation using the distributive property \(a(b + c)=ab+ac\).
For the left - hand side: \(-6(3x - 2)+4x=-6\times3x-6\times(-2)+4x=-18x + 12+4x\)
For the right - hand side: \(-4(x + 1)=-4\times x-4\times1=-4x-4\)
So the equation becomes \(-18x + 12+4x=-4x-4\)

Step2: Combine like terms

On the left - hand side, combine the \(x\) terms: \(-18x+4x=-14x\), so the left - hand side is \(-14x + 12\)
The equation is now \(-14x + 12=-4x-4\)

Step3: Isolate the \(x\) terms

Add \(14x\) to both sides of the equation to get all the \(x\) terms on one side:
\(-14x+14x + 12=-4x + 14x-4\)
Simplifying, we have \(12 = 10x-4\)

Step4: Solve for \(x\)

Add 4 to both sides of the equation: \(12 + 4=10x-4 + 4\)
\(16 = 10x\)
Then divide both sides by 10: \(x=\frac{16}{10}=\frac{8}{5}=1.6\)

Answer:

\(x = \frac{8}{5}\) (or \(x = 1.6\))