Solve for c 2c+6>5c-9

$2 c + 6 > 5 c - 9$

Step 1

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

Subtract $5 c$ from both sides of the inequality.

$2 c + 6 - 5 c > - 9$

Subtract $5 c$ from $2 c$ .

$- 3 c + 6 > - 9$

Step 2

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

Subtract $6$ from both sides of the inequality.

$- 3 c > - 9 - 6$

Subtract $6$ from $- 9$ .

$- 3 c > - 15$

Step 3

Divide each term in $- 3 c > - 15$ by $- 3$ and simplify.

Divide each term in $- 3 c > - 15$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 c}{- 3} < \frac{- 15}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 c}{- 3} < \frac{- 15}{- 3}$

Divide $c$ by $1$ .

$c < \frac{- 15}{- 3}$

Simplify the right side.

Divide $- 15$ by $- 3$ .

$c < 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$c < 5$

Interval Notation:

$(- \infty, 5)$

Solve for c 2c+6>5c-9

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