Solve the Inequality for c -7c-3(4c+5)>-5c+9+6

$- 7 c - 3 (4 c + 5) > - 5 c + 9 + 6$

Step 1

Simplify $- 7 c - 3 (4 c + 5)$ .

Simplify each term.

Apply the distributive property.

$- 7 c - 3 (4 c) - 3 \cdot 5 > - 5 c + 9 + 6$

Multiply $4$ by $- 3$ .

$- 7 c - 12 c - 3 \cdot 5 > - 5 c + 9 + 6$

Multiply $- 3$ by $5$ .

$- 7 c - 12 c - 15 > - 5 c + 9 + 6$

Subtract $12 c$ from $- 7 c$ .

$- 19 c - 15 > - 5 c + 9 + 6$

Step 2

Add $9$ and $6$ .

$- 19 c - 15 > - 5 c + 15$

Step 3

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

Add $5 c$ to both sides of the inequality.

$- 19 c - 15 + 5 c > 15$

Add $- 19 c$ and $5 c$ .

$- 14 c - 15 > 15$

Step 4

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

Add $15$ to both sides of the inequality.

$- 14 c > 15 + 15$

Add $15$ and $15$ .

$- 14 c > 30$

Step 5

Divide each term in $- 14 c > 30$ by $- 14$ and simplify.

Divide each term in $- 14 c > 30$ by $- 14$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 14 c}{- 14} < \frac{30}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 c}{- 14} < \frac{30}{- 14}$

Divide $c$ by $1$ .

$c < \frac{30}{- 14}$

Simplify the right side.

Cancel the common factor of $30$ and $- 14$ .

Factor $2$ out of $30$ .

$c < \frac{2 (15)}{- 14}$

Cancel the common factors.

Factor $2$ out of $- 14$ .

$c < \frac{2 \cdot 15}{2 \cdot - 7}$

Cancel the common factor.

$c < \frac{2 \cdot 15}{2 \cdot - 7}$

Rewrite the expression.

$c < \frac{15}{- 7}$

Move the negative in front of the fraction.

$c < - \frac{15}{7}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$c < - \frac{15}{7}$

Interval Notation:

$(- \infty, - \frac{15}{7})$

Solve the Inequality for c -7c-3(4c+5)>-5c+9+6

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