Solve the Inequality for c 10c+2(8c+10)<c-8-7

$10 c + 2 (8 c + 10) < c - 8 - 7$

Step 1

Simplify $10 c + 2 (8 c + 10)$ .

Simplify each term.

Apply the distributive property.

$10 c + 2 (8 c) + 2 \cdot 10 < c - 8 - 7$

Multiply $8$ by $2$ .

$10 c + 16 c + 2 \cdot 10 < c - 8 - 7$

Multiply $2$ by $10$ .

$10 c + 16 c + 20 < c - 8 - 7$

Add $10 c$ and $16 c$ .

$26 c + 20 < c - 8 - 7$

Step 2

Subtract $7$ from $- 8$ .

$26 c + 20 < c - 15$

Step 3

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

Subtract $c$ from both sides of the inequality.

$26 c + 20 - c < - 15$

Subtract $c$ from $26 c$ .

$25 c + 20 < - 15$

Step 4

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

Subtract $20$ from both sides of the inequality.

$25 c < - 15 - 20$

Subtract $20$ from $- 15$ .

$25 c < - 35$

Step 5

Divide each term in $25 c < - 35$ by $25$ and simplify.

Divide each term in $25 c < - 35$ by $25$ .

$\frac{25 c}{25} < \frac{- 35}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 c}{25} < \frac{- 35}{25}$

Divide $c$ by $1$ .

$c < \frac{- 35}{25}$

Simplify the right side.

Cancel the common factor of $- 35$ and $25$ .

Factor $5$ out of $- 35$ .

$c < \frac{5 (- 7)}{25}$

Cancel the common factors.

Factor $5$ out of $25$ .

$c < \frac{5 \cdot - 7}{5 \cdot 5}$

Cancel the common factor.

$c < \frac{5 \cdot - 7}{5 \cdot 5}$

Rewrite the expression.

$c < \frac{- 7}{5}$

Move the negative in front of the fraction.

$c < - \frac{7}{5}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$c < - \frac{7}{5}$

Interval Notation:

$(- \infty, - \frac{7}{5})$

Solve the Inequality for c 10c+2(8c+10)<c-8-7

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