Solve the Inequality for r -4r+4>=3r-4

$- 4 r + 4 \geq 3 r - 4$

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

Subtract $3 r$ from both sides of the inequality.

$- 4 r + 4 - 3 r \geq - 4$

Subtract $3 r$ from $- 4 r$ .

$- 7 r + 4 \geq - 4$

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

Subtract $4$ from both sides of the inequality.

$- 7 r \geq - 4 - 4$

Subtract $4$ from $- 4$ .

$- 7 r \geq - 8$

Divide each term in $- 7 r \geq - 8$ by $- 7$ and simplify.

Divide each term in $- 7 r \geq - 8$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 r}{- 7} \leq \frac{- 8}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 r}{- 7} \leq \frac{- 8}{- 7}$

Divide $r$ by $1$ .

$r \leq \frac{- 8}{- 7}$

Simplify the right side.

Dividing two negative values results in a positive value.

$r \leq \frac{8}{7}$

The result can be shown in multiple forms.

Inequality Form:

$r \leq \frac{8}{7}$

Interval Notation:

$(- \infty, \frac{8}{7}]$

Solve the Inequality for r -4r+4>=3r-4

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