Solve for y -2(y-2)<2(y-4)

$- 2 (y - 2) < 2 (y - 4)$

Step 1

Simplify $- 2 (y - 2)$ .

Rewrite.

$0 + 0 - 2 (y - 2) < 2 (y - 4)$

Simplify by adding zeros.

$- 2 (y - 2) < 2 (y - 4)$

Apply the distributive property.

$- 2 y - 2 \cdot - 2 < 2 (y - 4)$

Multiply $- 2$ by $- 2$ .

$- 2 y + 4 < 2 (y - 4)$

Step 2

Simplify $2 (y - 4)$ .

Apply the distributive property.

$- 2 y + 4 < 2 y + 2 \cdot - 4$

Multiply $2$ by $- 4$ .

$- 2 y + 4 < 2 y - 8$

Step 3

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

Subtract $2 y$ from both sides of the inequality.

$- 2 y + 4 - 2 y < - 8$

Subtract $2 y$ from $- 2 y$ .

$- 4 y + 4 < - 8$

Step 4

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

Subtract $4$ from both sides of the inequality.

$- 4 y < - 8 - 4$

Subtract $4$ from $- 8$ .

$- 4 y < - 12$

Step 5

Divide each term in $- 4 y < - 12$ by $- 4$ and simplify.

Divide each term in $- 4 y < - 12$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} > \frac{- 12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} > \frac{- 12}{- 4}$

Divide $y$ by $1$ .

$y > \frac{- 12}{- 4}$

Simplify the right side.

Divide $- 12$ by $- 4$ .

$y > 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$y > 3$

Interval Notation:

$(3, \infty)$

Solve for y -2(y-2)<2(y-4)

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