Question

solve for g.
4(g - 2) - 11 ≥ 1

Explanation:

Step1: Expand the left - hand side

First, we use the distributive property \(a(b - c)=ab - ac\) to expand \(4(g - 2)\). So \(4(g - 2)=4g-8\). The inequality becomes \(4g - 8-11\geq1\).

Step2: Simplify the left - hand side

Combine like terms on the left - hand side. \(-8-11=-19\), so the inequality is \(4g-19\geq1\).

Step3: Isolate the term with g

Add 19 to both sides of the inequality. According to the addition property of inequalities (if \(a\geq b\), then \(a + c\geq b + c\)), we have \(4g-19 + 19\geq1 + 19\), which simplifies to \(4g\geq20\).

Step4: Solve for g

Divide both sides of the inequality by 4. According to the division property of inequalities (if \(a\geq b\) and \(c>0\), then \(\frac{a}{c}\geq\frac{b}{c}\)), we get \(\frac{4g}{4}\geq\frac{20}{4}\), so \(g\geq5\).

Answer:

\(g\geq5\)