Question

solve the inequality and graph the solution.
5(j + 4) ≤ 15
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b + c)=ab+ac\). Here \(a = 5\), \(b=j\), \(c = 4\).
\(5(j + 4)=5j+20\). So the inequality becomes \(5j+20\leq15\).

Step2: Subtract 20 from both sides

To isolate the term with \(j\), use the subtraction property of inequalities.
\(5j+20 - 20\leq15 - 20\).
\(5j\leq-5\).

Step3: Divide both sides by 5

Use the division property of inequalities. Since \(5>0\), the direction of the inequality sign does not change.
\(\frac{5j}{5}\leq\frac{-5}{5}\).
\(j\leq - 1\).

Answer:

The solution of the inequality \(5(j + 4)\leq15\) is \(j\leq - 1\). On the number - line, we have a closed circle at \(-1\) (because the inequality is \(\leq\)) and the line extends to the left (towards \(-\infty\)).