Question

-5x - 4(3x - 10) > 40 - 2x

Explanation:

Step1: Expand the left - hand side

We use the distributive property \(a(b + c)=ab+ac\) (here \(a=- 4\), \(b = 3x\), \(c=-10\)) to expand \(-4(3x - 10)\).
\(-5x-4(3x - 10)=-5x-12x + 40\)
So the inequality becomes \(-5x-12x + 40>40-2x\)

Step2: Combine like terms on the left - hand side

Combine \(-5x\) and \(-12x\): \(-5x-12x=-17x\)
The inequality is now \(-17x + 40>40-2x\)

Step3: Move all \(x\) terms to one side and constants to the other side

Subtract \(40\) from both sides: \(-17x+40 - 40>40-2x - 40\), which simplifies to \(-17x>-2x\)
Then add \(2x\) to both sides: \(-17x + 2x>-2x+2x\), which gives \(-15x>0\)

Step4: Solve for \(x\)

Divide both sides of the inequality \(-15x>0\) by \(-15\). Remember that when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes.
So \(x <\frac{0}{-15}\), which simplifies to \(x < 0\)

Answer:

\(x < 0\)