Solve the Inequality for h 6h-5(h-1)<=7h-11

$6 h - 5 (h - 1) \leq 7 h - 11$

Simplify $6 h - 5 (h - 1)$ .

Simplify each term.

Apply the distributive property.

$6 h - 5 h - 5 \cdot - 1 \leq 7 h - 11$

Multiply $- 5$ by $- 1$ .

$6 h - 5 h + 5 \leq 7 h - 11$

Subtract $5 h$ from $6 h$ .

$h + 5 \leq 7 h - 11$

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

Subtract $7 h$ from both sides of the inequality.

$h + 5 - 7 h \leq - 11$

Subtract $7 h$ from $h$ .

$- 6 h + 5 \leq - 11$

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

Subtract $5$ from both sides of the inequality.

$- 6 h \leq - 11 - 5$

Subtract $5$ from $- 11$ .

$- 6 h \leq - 16$

Divide each term in $- 6 h \leq - 16$ by $- 6$ and simplify.

Divide each term in $- 6 h \leq - 16$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 h}{- 6} \geq \frac{- 16}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 h}{- 6} \geq \frac{- 16}{- 6}$

Divide $h$ by $1$ .

$h \geq \frac{- 16}{- 6}$

Simplify the right side.

Cancel the common factor of $- 16$ and $- 6$ .

Factor $- 2$ out of $- 16$ .

$h \geq \frac{- 2 (8)}{- 6}$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

$h \geq \frac{- 2 \cdot 8}{- 2 \cdot 3}$

Cancel the common factor.

$h \geq \frac{- 2 \cdot 8}{- 2 \cdot 3}$

Rewrite the expression.

$h \geq \frac{8}{3}$

The result can be shown in multiple forms.

Inequality Form:

$h \geq \frac{8}{3}$

Interval Notation:

$[\frac{8}{3}, \infty)$

Solve the Inequality for h 6h-5(h-1)<=7h-11

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