Question

solve for c.

c - 11 < -11 + 6c or -16c + 3 + 18c ≤ 1

write your answer as a compound inequality with integers.

Explanation:

Step1: Solve the first inequality

Subtract \(c\) from both sides of \(c - 11 < -11+6c\):
\(c - 11 - c< - 11+6c - c\)
\(-11 < - 11 + 5c\)
Add 11 to both sides:
\(-11+11 < - 11 + 11+5c\)
\(0 < 5c\)
Divide both sides by 5:
\(\frac{0}{5}<\frac{5c}{5}\)
\(0 < c\)

Step2: Solve the second inequality

Combine like - terms in \(-16c + 3+18c\leq1\):
\((-16c + 18c)+3\leq1\)
\(2c+3\leq1\)
Subtract 3 from both sides:
\(2c+3 - 3\leq1 - 3\)
\(2c\leq - 2\)
Divide both sides by 2:
\(\frac{2c}{2}\leq\frac{-2}{2}\)
\(c\leq - 1\)

Answer:

\(c\leq - 1\) or \(c > 0\)