Question

svlc algebra 1a - standard (15260)
solving one - variable inequalities
solve the inequality.
$2(4 + 2x) \geq 5x + 5$
options: $x \geq 3$, $x \geq - 2$, $x \leq 3$, $x \leq - 2$

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), we expand \(2(4 + 2x)\) to get \(2\times4+2\times2x = 8 + 4x\). So the inequality becomes \(8 + 4x\geq5x + 5\).

Step2: Move variable terms to one side

Subtract \(4x\) from both sides of the inequality: \(8+4x - 4x\geq5x + 5-4x\), 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 equivalently \(x\leq3\).

Answer:

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