Solve the Inequality for h 4(3h-7)<=20(h-1)

$4 (3 h - 7) \leq 20 (h - 1)$

Simplify $4 (3 h - 7)$ .

Start simplifying.

$0 + 0 + 4 (3 h - 7) \leq 20 (h - 1)$

Simplify by adding zeros.

$4 (3 h - 7) \leq 20 (h - 1)$

Apply the distributive property.

$4 (3 h) + 4 \cdot - 7 \leq 20 (h - 1)$

Multiply.

Multiply $3$ by $4$ .

$12 h + 4 \cdot - 7 \leq 20 (h - 1)$

Multiply $4$ by $- 7$ .

$12 h - 28 \leq 20 (h - 1)$

Simplify $20 (h - 1)$ .

Apply the distributive property.

$12 h - 28 \leq 20 h + 20 \cdot - 1$

Multiply $20$ by $- 1$ .

$12 h - 28 \leq 20 h - 20$

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

Subtract $20 h$ from both sides of the inequality.

$12 h - 28 - 20 h \leq - 20$

Subtract $20 h$ from $12 h$ .

$- 8 h - 28 \leq - 20$

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

Add $28$ to both sides of the inequality.

$- 8 h \leq - 20 + 28$

Add $- 20$ and $28$ .

$- 8 h \leq 8$

Divide each term in $- 8 h \leq 8$ by $- 8$ and simplify.

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

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

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

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

Divide $h$ by $1$ .

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

Simplify the right side.

Divide $8$ by $- 8$ .

$h \geq - 1$

The result can be shown in multiple forms.

Inequality Form:

$h \geq - 1$

Interval Notation:

$[- 1, \infty)$

Solve the Inequality for h 4(3h-7)<=20(h-1)

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