Solve the Inequality for c -1/2c+5<=7

$- \frac{1}{2} c + 5 \leq 7$

Combine $c$ and $\frac{1}{2}$ .

$- \frac{c}{2} + 5 \leq 7$

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

Subtract $5$ from both sides of the inequality.

$- \frac{c}{2} \leq 7 - 5$

Subtract $5$ from $7$ .

$- \frac{c}{2} \leq 2$

Divide each term in $- \frac{c}{2} \leq 2$ by $- 1$ and simplify.

Divide each term in $- \frac{c}{2} \leq 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{c}{2}}{- 1} \geq \frac{2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{c}{2}}{1} \geq \frac{2}{- 1}$

Divide $\frac{c}{2}$ by $1$ .

$\frac{c}{2} \geq \frac{2}{- 1}$

Simplify the right side.

Divide $2$ by $- 1$ .

$\frac{c}{2} \geq - 2$

Multiply both sides by $2$ .

$\frac{c}{2} \cdot 2 \geq - 2 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{c}{2} \cdot 2 \geq - 2 \cdot 2$

Rewrite the expression.

$c \geq - 2 \cdot 2$

Simplify the right side.

Multiply $- 2$ by $2$ .

$c \geq - 4$

The result can be shown in multiple forms.

Inequality Form:

$c \geq - 4$

Interval Notation:

$[- 4, \infty)$

Solve the Inequality for c -1/2c+5<=7

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