Solve the Inequality for c 5c+3>=6c-8

$5 c + 3 \geq 6 c - 8$

Step 1

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

Subtract $6 c$ from both sides of the inequality.

$5 c + 3 - 6 c \geq - 8$

Subtract $6 c$ from $5 c$ .

$- c + 3 \geq - 8$

Step 2

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

Subtract $3$ from both sides of the inequality.

$- c \geq - 8 - 3$

Subtract $3$ from $- 8$ .

$- c \geq - 11$

Step 3

Divide each term in $- c \geq - 11$ by $- 1$ and simplify.

Divide each term in $- c \geq - 11$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- c}{- 1} \leq \frac{- 11}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{c}{1} \leq \frac{- 11}{- 1}$

Divide $c$ by $1$ .

$c \leq \frac{- 11}{- 1}$

Simplify the right side.

Divide $- 11$ by $- 1$ .

$c \leq 11$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$c \leq 11$

Interval Notation:

$(- \infty, 11]$

Solve the Inequality for c 5c+3>=6c-8

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