Question

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

Explanation:

Step1: Expand the left side

First, we expand the left - hand side of the inequality \(2(4 + 2x)\geq5x + 5\) using the distributive property \(a(b + c)=ab+ac\). Here, \(a = 2\), \(b = 4\) and \(c = 2x\), so \(2\times4+2\times2x\geq5x + 5\), which simplifies to \(8 + 4x\geq5x+5\).

Step2: Move the terms with x to one side

Subtract \(4x\) from both sides of the inequality: \(8+4x - 4x\geq5x + 5-4x\). This gives us \(8\geq x + 5\).

Step3: Solve for x

Subtract 5 from both sides of the inequality \(8-5\geq x+5 - 5\). So, \(3\geq x\), which is equivalent to \(x\leq3\).

Answer:

\(x\leq3\) (corresponding to the option \(x\leq3\))