Question

solve the inequality.
2(4+2x)≥5x+5
○ x≤−2
○ x≥−2
○ x≤3
○ x≥3

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(2(4 + 2x)\) to get \(8+4x\). So the inequality becomes \(8 + 4x\geq5x + 5\).

Step2: Move terms with x to one side

Subtract \(4x\) from both sides: \(8+4x - 4x\geq5x + 5-4x\), which simplifies to \(8\geq x + 5\).

Step3: Solve for x

Subtract 5 from both sides: \(8 - 5\geq x+5 - 5\), so \(3\geq x\) or \(x\leq3\).

Answer:

\(x\leq3\) (corresponding to the option "x≤3")