Solve for r 167<6+7(2-7r)

$167 < 6 + 7 (2 - 7 r)$

Step 1

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

$6 + 7 (2 - 7 r) > 167$

Step 2

Simplify $6 + 7 (2 - 7 r)$ .

Simplify each term.

Apply the distributive property.

$6 + 7 \cdot 2 + 7 (- 7 r) > 167$

Multiply $7$ by $2$ .

$6 + 14 + 7 (- 7 r) > 167$

Multiply $- 7$ by $7$ .

$6 + 14 - 49 r > 167$

Add $6$ and $14$ .

$20 - 49 r > 167$

Step 3

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

Subtract $20$ from both sides of the inequality.

$- 49 r > 167 - 20$

Subtract $20$ from $167$ .

$- 49 r > 147$

Step 4

Divide each term in $- 49 r > 147$ by $- 49$ and simplify.

Divide each term in $- 49 r > 147$ by $- 49$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 49 r}{- 49} < \frac{147}{- 49}$

Simplify the left side.

Cancel the common factor of $- 49$ .

Cancel the common factor.

$\frac{- 49 r}{- 49} < \frac{147}{- 49}$

Divide $r$ by $1$ .

$r < \frac{147}{- 49}$

Simplify the right side.

Divide $147$ by $- 49$ .

$r < - 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$r < - 3$

Interval Notation:

$(- \infty, - 3)$

Solve for r 167<6+7(2-7r)

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