Solve the Inequality for c 55c+13<=75c+39

$55 c + 13 \leq 75 c + 39$

Step 1

Move all terms containing $c$ to the left side of the inequality.

Subtract $75 c$ from both sides of the inequality.

$55 c + 13 - 75 c \leq 39$

Subtract $75 c$ from $55 c$ .

$- 20 c + 13 \leq 39$

Step 2

Move all terms not containing $c$ to the right side of the inequality.

Subtract $13$ from both sides of the inequality.

$- 20 c \leq 39 - 13$

Subtract $13$ from $39$ .

$- 20 c \leq 26$

Step 3

Divide each term in $- 20 c \leq 26$ by $- 20$ and simplify.

Divide each term in $- 20 c \leq 26$ by $- 20$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 20 c}{- 20} \geq \frac{26}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 c}{- 20} \geq \frac{26}{- 20}$

Divide $c$ by $1$ .

$c \geq \frac{26}{- 20}$

Simplify the right side.

Cancel the common factor of $26$ and $- 20$ .

Factor $2$ out of $26$ .

$c \geq \frac{2 (13)}{- 20}$

Cancel the common factors.

Factor $2$ out of $- 20$ .

$c \geq \frac{2 \cdot 13}{2 \cdot - 10}$

Cancel the common factor.

$c \geq \frac{2 \cdot 13}{2 \cdot - 10}$

Rewrite the expression.

$c \geq \frac{13}{- 10}$

Move the negative in front of the fraction.

$c \geq - \frac{13}{10}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$c \geq - \frac{13}{10}$

Interval Notation:

$[- \frac{13}{10}, \infty)$

Solve the Inequality for c 55c+13<=75c+39

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