Solve the Inequality for c 7-3(6c+14)>5(1-2c)

$7 - 3 (6 c + 14) > 5 (1 - 2 c)$

Step 1

Simplify $7 - 3 (6 c + 14)$ .

Simplify each term.

Apply the distributive property.

$7 - 3 (6 c) - 3 \cdot 14 > 5 (1 - 2 c)$

Multiply $6$ by $- 3$ .

$7 - 18 c - 3 \cdot 14 > 5 (1 - 2 c)$

Multiply $- 3$ by $14$ .

$7 - 18 c - 42 > 5 (1 - 2 c)$

Subtract $42$ from $7$ .

$- 18 c - 35 > 5 (1 - 2 c)$

Step 2

Simplify $5 (1 - 2 c)$ .

Apply the distributive property.

$- 18 c - 35 > 5 \cdot 1 + 5 (- 2 c)$

Multiply.

Multiply $5$ by $1$ .

$- 18 c - 35 > 5 + 5 (- 2 c)$

Multiply $- 2$ by $5$ .

$- 18 c - 35 > 5 - 10 c$

Step 3

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

Add $10 c$ to both sides of the inequality.

$- 18 c - 35 + 10 c > 5$

Add $- 18 c$ and $10 c$ .

$- 8 c - 35 > 5$

Step 4

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

Add $35$ to both sides of the inequality.

$- 8 c > 5 + 35$

Add $5$ and $35$ .

$- 8 c > 40$

Step 5

Divide each term in $- 8 c > 40$ by $- 8$ and simplify.

Divide each term in $- 8 c > 40$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 c}{- 8} < \frac{40}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 c}{- 8} < \frac{40}{- 8}$

Divide $c$ by $1$ .

$c < \frac{40}{- 8}$

Simplify the right side.

Divide $40$ by $- 8$ .

$c < - 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$c < - 5$

Interval Notation:

$(- \infty, - 5)$

Solve the Inequality for c 7-3(6c+14)>5(1-2c)

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