Solve the Inequality for b 35<7(2-b)

$35 < 7 (2 - b)$

Step 1

Rewrite so $b$ is on the left side of the inequality.

$7 (2 - b) > 35$

Step 2

Divide each term in $7 (2 - b) > 35$ by $7$ and simplify.

Divide each term in $7 (2 - b) > 35$ by $7$ .

$\frac{7 (2 - b)}{7} > \frac{35}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 (2 - b)}{7} > \frac{35}{7}$

Divide $2 - b$ by $1$ .

$2 - b > \frac{35}{7}$

Simplify the right side.

Divide $35$ by $7$ .

$2 - b > 5$

Step 3

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

Subtract $2$ from both sides of the inequality.

$- b > 5 - 2$

Subtract $2$ from $5$ .

$- b > 3$

Step 4

Divide each term in $- b > 3$ by $- 1$ and simplify.

Divide each term in $- b > 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- b}{- 1} < \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{b}{1} < \frac{3}{- 1}$

Divide $b$ by $1$ .

$b < \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$b < - 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$b < - 3$

Interval Notation:

$(- \infty, - 3)$

Solve the Inequality for b 35<7(2-b)

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