Solve for 
\[c\].
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
\[55c+13 \leq 75c + 39\]


We are given the inequality:

\[
55c + 13 \leq 75c + 39
\]

### Step 1: Move all terms involving \( c \) to one side
Subtract \( 55c \) from both sides:

\[
13 \leq 20c + 39
\]

### Step 2: Move the constant term to the other side
Subtract 39 from both sides:

\[
13 - 39 \leq 20c
\]

Simplifying:

\[
-26 \leq 20c
\]

### Step 3: Solve for \( c \)
Divide both sides by 20:

\[
\frac{-26}{20} \leq c
\]

### Step 4: Reduce the fraction
Simplify \( \frac{-26}{20} \):

\[
c \geq \frac{-13}{10}
\]

Thus, the solution is:

\[
c \geq \frac{-13}{10}
\]

Would you like more details on any part of this solution?

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Here are five related questions:
1. How do you solve inequalities involving multiple variables?
2. What happens if you multiply or divide both sides of an inequality by a negative number?
3. Can you graph the solution of \( c \geq \frac{-13}{10} \)?
4. How would you solve \( 55c + 13 > 75c + 39 \)?
5. Can you apply these techniques to quadratic inequalities?

**Tip:** Always remember that reversing the inequality sign happens when multiplying or dividing by a negative number.

Solve for c. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. 55c + 13 ≤ 75c + 39.

Learn how to solve the linear inequality 55c + 13 ≤ 75c + 39 step-by-step. This tutorial covers essential algebraic concepts, including moving terms, solving inequalities, and simplifying fractions. Perfect for students in Grades 8-10.

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