Solve the Inequality for h -h+3(5h-7)<2h+5+5h

$- h + 3 (5 h - 7) < 2 h + 5 + 5 h$

Step 1

Simplify $- h + 3 (5 h - 7)$ .

Simplify each term.

Apply the distributive property.

$- h + 3 (5 h) + 3 \cdot - 7 < 2 h + 5 + 5 h$

Multiply $5$ by $3$ .

$- h + 15 h + 3 \cdot - 7 < 2 h + 5 + 5 h$

Multiply $3$ by $- 7$ .

$- h + 15 h - 21 < 2 h + 5 + 5 h$

Add $- h$ and $15 h$ .

$14 h - 21 < 2 h + 5 + 5 h$

Step 2

Add $2 h$ and $5 h$ .

$14 h - 21 < 7 h + 5$

Step 3

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

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

$14 h - 21 - 7 h < 5$

Subtract $7 h$ from $14 h$ .

$7 h - 21 < 5$

Step 4

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

Add $21$ to both sides of the inequality.

$7 h < 5 + 21$

Add $5$ and $21$ .

$7 h < 26$

Step 5

Divide each term in $7 h < 26$ by $7$ and simplify.

Divide each term in $7 h < 26$ by $7$ .

$\frac{7 h}{7} < \frac{26}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 h}{7} < \frac{26}{7}$

Divide $h$ by $1$ .

$h < \frac{26}{7}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$h < \frac{26}{7}$

Interval Notation:

$(- \infty, \frac{26}{7})$