Solve the Inequality for r 5-3(-7r+1)>-5r-3+9r

$5 - 3 (- 7 r + 1) > - 5 r - 3 + 9 r$

Step 1

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

$- 5 r - 3 + 9 r < 5 - 3 (- 7 r + 1)$

Step 2

Add $- 5 r$ and $9 r$ .

$4 r - 3 < 5 - 3 (- 7 r + 1)$

Step 3

Simplify $5 - 3 (- 7 r + 1)$ .

Simplify each term.

Apply the distributive property.

$4 r - 3 < 5 - 3 (- 7 r) - 3 \cdot 1$

Multiply $- 7$ by $- 3$ .

$4 r - 3 < 5 + 21 r - 3 \cdot 1$

Multiply $- 3$ by $1$ .

$4 r - 3 < 5 + 21 r - 3$

Subtract $3$ from $5$ .

$4 r - 3 < 21 r + 2$

Step 4

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

Subtract $21 r$ from both sides of the inequality.

$4 r - 3 - 21 r < 2$

Subtract $21 r$ from $4 r$ .

$- 17 r - 3 < 2$

Step 5

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

Add $3$ to both sides of the inequality.

$- 17 r < 2 + 3$

Add $2$ and $3$ .

$- 17 r < 5$

Step 6

Divide each term in $- 17 r < 5$ by $- 17$ and simplify.

Divide each term in $- 17 r < 5$ by $- 17$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 17 r}{- 17} > \frac{5}{- 17}$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 r}{- 17} > \frac{5}{- 17}$

Divide $r$ by $1$ .

$r > \frac{5}{- 17}$

Simplify the right side.

Move the negative in front of the fraction.

$r > - \frac{5}{17}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$r > - \frac{5}{17}$

Interval Notation:

$(- \frac{5}{17}, \infty)$

Solve the Inequality for r 5-3(-7r+1)>-5r-3+9r

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