Solve the Inequality for b 10b+7<5b+8

$10 b + 7 < 5 b + 8$

Step 1

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

Subtract $5 b$ from both sides of the inequality.

$10 b + 7 - 5 b < 8$

Subtract $5 b$ from $10 b$ .

$5 b + 7 < 8$

Step 2

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

Subtract $7$ from both sides of the inequality.

$5 b < 8 - 7$

Subtract $7$ from $8$ .

$5 b < 1$

Step 3

Divide each term in $5 b < 1$ by $5$ and simplify.

Divide each term in $5 b < 1$ by $5$ .

$\frac{5 b}{5} < \frac{1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 b}{5} < \frac{1}{5}$

Divide $b$ by $1$ .

$b < \frac{1}{5}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$b < \frac{1}{5}$

Interval Notation:

$(- \infty, \frac{1}{5})$