Question

solve the inequality and graph the solution.
9(c + 1) + 10 ≤ 1
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.
submit

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b + c)=ab+ac\). Here \(a = 9\), \(b=c\), \(c = 1\).
\(9(c + 1)+10=9c+9 + 10=9c+19\)
The inequality becomes \(9c+19\leq1\).

Step2: Subtract 19 from both sides

To isolate the term with \(c\), use the subtraction property of inequalities.
\(9c+19-19\leq1 - 19\)
\(9c\leq-18\)

Step3: Divide both sides by 9

Use the division property of inequalities. Since \(9>0\), the direction of the inequality sign does not change.
\(\frac{9c}{9}\leq\frac{-18}{9}\)
\(c\leq - 2\)

Answer:

The solution of the inequality \(9(c + 1)+10\leq1\) is \(c\leq - 2\). On the number - line, we plot a closed circle at \(-2\) (because the inequality is \(\leq\)) and draw a ray to the left of \(-2\).