Solve the Inequality for r -7r-4>=4r+2

$- 7 r - 4 \geq 4 r + 2$

Step 1

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

Subtract $4 r$ from both sides of the inequality.

$- 7 r - 4 - 4 r \geq 2$

Subtract $4 r$ from $- 7 r$ .

$- 11 r - 4 \geq 2$

Step 2

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

Add $4$ to both sides of the inequality.

$- 11 r \geq 2 + 4$

Add $2$ and $4$ .

$- 11 r \geq 6$

Step 3

Divide each term in $- 11 r \geq 6$ by $- 11$ and simplify.

Divide each term in $- 11 r \geq 6$ by $- 11$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 11 r}{- 11} \leq \frac{6}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 r}{- 11} \leq \frac{6}{- 11}$

Divide $r$ by $1$ .

$r \leq \frac{6}{- 11}$

Simplify the right side.

Move the negative in front of the fraction.

$r \leq - \frac{6}{11}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$r \leq - \frac{6}{11}$

Interval Notation:

$(- \infty, - \frac{6}{11}]$

Solve the Inequality for r -7r-4>=4r+2

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