Question

solve for j.
2(j + 12) + 2 ≥ 20

Explanation:

Step1: Simplify the left - hand side

First, expand the expression \(2(j + 12)+2\). Using the distributive property \(a(b + c)=ab+ac\), we have \(2(j + 12)=2j+24\). Then the left - hand side becomes \(2j + 24+2=2j+26\). So the inequality is \(2j + 26\geq20\).

Step2: Isolate the variable term

Subtract 26 from both sides of the inequality. According to the subtraction property of inequalities (if \(a\geq b\), then \(a - c\geq b - c\) for any real number \(c\)), we get \(2j+26 - 26\geq20 - 26\), which simplifies to \(2j\geq - 6\).

Step3: Solve for j

Divide both sides of the inequality \(2j\geq - 6\) by 2. Using the division property of inequalities (if \(a\geq b\) and \(c>0\), then \(\frac{a}{c}\geq\frac{b}{c}\)), we have \(\frac{2j}{2}\geq\frac{-6}{2}\), so \(j\geq - 3\).

Answer:

\(j\geq - 3\)