Solve for y 4y+5>5y+12

$4 y + 5 > 5 y + 12$

Step 1

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

Subtract $5 y$ from both sides of the inequality.

$4 y + 5 - 5 y > 12$

Subtract $5 y$ from $4 y$ .

$- y + 5 > 12$

Step 2

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

Subtract $5$ from both sides of the inequality.

$- y > 12 - 5$

Subtract $5$ from $12$ .

$- y > 7$

Step 3

Divide each term in $- y > 7$ by $- 1$ and simplify.

Divide each term in $- y > 7$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} < \frac{7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} < \frac{7}{- 1}$

Divide $y$ by $1$ .

$y < \frac{7}{- 1}$

Simplify the right side.

Divide $7$ by $- 1$ .

$y < - 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y < - 7$

Interval Notation:

$(- \infty, - 7)$

Solve for y 4y+5>5y+12

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