Question

linear inequalities (level 1)
question
solve the following inequality for c. write your answer in simplest form.
$c - 8 < 10c + 3$

Explanation:

Step1: Subtract \( c \) from both sides

To isolate the variable terms, subtract \( c \) from both sides of the inequality \( c - 8 < 10c + 3 \). This gives \( c - c - 8 < 10c - c + 3 \), which simplifies to \( -8 < 9c + 3 \).

Step2: Subtract 3 from both sides

Subtract 3 from both sides to get \( -8 - 3 < 9c + 3 - 3 \), so \( -11 < 9c \).

Step3: Divide by 9

Divide both sides by 9: \( \frac{-11}{9} < c \), or \( c > -\frac{11}{9} \).

Answer:

\( c > -\frac{11}{9} \)