Question

4x - 24 + 4 > 5x - 12
4x - 20 > 5x - 12
-4x -4x
-20 > x - 12
+12 +12
-8 > x
x < -8

-2(3x - 4) - (x + 2) ≥ -15

Explanation:

Step1: Expand the brackets

First, we expand the terms in the inequality \(-2(3x - 4)-(x + 2)\geq - 15\). Using the distributive property \(a(b + c)=ab+ac\), we have:
\(-2\times3x-2\times(-4)-x - 2\geq - 15\)
\(-6x + 8-x - 2\geq - 15\)

Step2: Combine like terms

Next, we combine the like - terms on the left - hand side. Combine the \(x\) terms and the constant terms:
\((-6x-x)+(8 - 2)\geq - 15\)
\(-7x+6\geq - 15\)

Step3: Isolate the variable term

Subtract 6 from both sides of the inequality to isolate the term with \(x\):
\(-7x+6 - 6\geq - 15-6\)
\(-7x\geq - 21\)

Step4: Solve for \(x\)

Divide both sides of the inequality by \(-7\). Remember that when we divide or multiply an inequality by a negative number, the direction of the inequality sign changes. So we have:
\(\frac{-7x}{-7}\leq\frac{-21}{-7}\)
\(x\leq3\)

Answer:

\(x\leq3\)