Graph 2(1-4r)<-2(r+3)-4

$2 (1 - 4 r) < - 2 (r + 3) - 4$

Step 1

Simplify $2 (1 - 4 r)$ .

Rewrite.

$0 + 0 + 2 (1 - 4 r) < - 2 (r + 3) - 4$

Simplify by adding zeros.

$2 (1 - 4 r) < - 2 (r + 3) - 4$

Apply the distributive property.

$2 \cdot 1 + 2 (- 4 r) < - 2 (r + 3) - 4$

Multiply.

Multiply $2$ by $1$ .

$2 + 2 (- 4 r) < - 2 (r + 3) - 4$

Multiply $- 4$ by $2$ .

$2 - 8 r < - 2 (r + 3) - 4$

Step 2

Simplify $- 2 (r + 3) - 4$ .

Simplify each term.

Apply the distributive property.

$2 - 8 r < - 2 r - 2 \cdot 3 - 4$

Multiply $- 2$ by $3$ .

$2 - 8 r < - 2 r - 6 - 4$

Subtract $4$ from $- 6$ .

$2 - 8 r < - 2 r - 10$

Step 3

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

Add $2 r$ to both sides of the inequality.

$2 - 8 r + 2 r < - 10$

Add $- 8 r$ and $2 r$ .

$2 - 6 r < - 10$

Step 4

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

Subtract $2$ from both sides of the inequality.

$- 6 r < - 10 - 2$

Subtract $2$ from $- 10$ .

$- 6 r < - 12$

Step 5

Divide each term in $- 6 r < - 12$ by $- 6$ and simplify.

Divide each term in $- 6 r < - 12$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 r}{- 6} > \frac{- 12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 r}{- 6} > \frac{- 12}{- 6}$

Divide $r$ by $1$ .

$r > \frac{- 12}{- 6}$

Simplify the right side.

Divide $- 12$ by $- 6$ .

$r > 2$

Step 6

Graph 2(1-4r)<-2(r+3)-4

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