Question

solve the inequality and graph the solution. -8x + 4 ≥ 4(6 - x). choose the correct graph below. a. graph with open - circle at - 6 and arrow pointing down c. graph with closed - circle at - 6 and arrow pointing up the solution is (type an inequality)

Explanation:

Step1: Expand the right - hand side

First, expand \(4(6 - x)\) using the distributive property \(a(b - c)=ab - ac\). So \(4(6 - x)=24-4x\). The inequality becomes \(-8x + 4\geq24 - 4x\).

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

Add \(8x\) to both sides of the inequality: \(-8x+8x + 4\geq24-4x + 8x\), which simplifies to \(4\geq24 + 4x\).

Step3: Move the constant terms to one side

Subtract 24 from both sides: \(4-24\geq24 - 24+4x\), resulting in \(-20\geq4x\).

Step4: Solve for \(x\)

Divide both sides by 4: \(\frac{-20}{4}\geq\frac{4x}{4}\), so \(x\leq - 5\).

The solution of the inequality \(x\leq - 5\) is represented on a number - line with a closed circle at \(-5\) (because the inequality is \(\leq\)) and the line extending to the left.

Answer:

The solution is \(x\leq - 5\). The correct graph is the one with a closed - circle at \(-5\) and the arrow pointing to the left.