Solve the Inequality for c -7c-(8c-9)>6c+1-2c

$- 7 c - (8 c - 9) > 6 c + 1 - 2 c$

Step 1

Simplify $- 7 c - (8 c - 9)$ .

Simplify each term.

Apply the distributive property.

$- 7 c - (8 c) - - 9 > 6 c + 1 - 2 c$

Multiply $8$ by $- 1$ .

$- 7 c - 8 c - - 9 > 6 c + 1 - 2 c$

Multiply $- 1$ by $- 9$ .

$- 7 c - 8 c + 9 > 6 c + 1 - 2 c$

Subtract $8 c$ from $- 7 c$ .

$- 15 c + 9 > 6 c + 1 - 2 c$

Step 2

Subtract $2 c$ from $6 c$ .

$- 15 c + 9 > 4 c + 1$

Step 3

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

Subtract $4 c$ from both sides of the inequality.

$- 15 c + 9 - 4 c > 1$

Subtract $4 c$ from $- 15 c$ .

$- 19 c + 9 > 1$

Step 4

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

Subtract $9$ from both sides of the inequality.

$- 19 c > 1 - 9$

Subtract $9$ from $1$ .

$- 19 c > - 8$

Step 5

Divide each term in $- 19 c > - 8$ by $- 19$ and simplify.

Divide each term in $- 19 c > - 8$ by $- 19$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 19 c}{- 19} < \frac{- 8}{- 19}$

Simplify the left side.

Cancel the common factor of $- 19$ .

Cancel the common factor.

$\frac{- 19 c}{- 19} < \frac{- 8}{- 19}$

Divide $c$ by $1$ .

$c < \frac{- 8}{- 19}$

Simplify the right side.

Dividing two negative values results in a positive value.

$c < \frac{8}{19}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$c < \frac{8}{19}$

Interval Notation:

$(- \infty, \frac{8}{19})$

Solve the Inequality for c -7c-(8c-9)>6c+1-2c

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