Question

solve the inequality and graph the solution.
16(c + 1) - 20 < 12
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: Simplify the left - hand side

Use the distributive property \(a(b + c)=ab+ac\).
\(16(c + 1)-20=16c+16 - 20=16c - 4\).
The inequality becomes \(16c-4\lt12\).

Step2: Add 4 to both sides

To isolate the term with \(c\), add 4 to both sides of the inequality.
\(16c-4 + 4\lt12 + 4\), which simplifies to \(16c\lt16\).

Step3: Divide both sides by 16

Divide both sides of the inequality \(16c\lt16\) by 16.
\(\frac{16c}{16}\lt\frac{16}{16}\), so \(c\lt1\).

Answer:

The solution of the inequality \(16(c + 1)-20\lt12\) is \(c\lt1\). On the number - line, we have an open circle at \(c = 1\) (since the inequality is strict, \(c
eq1\)) and the line extends to the left of \(1\) towards \(-\infty\).