Solve the Inequality for y (5-2y)/12>1-6y

$\frac{5 - 2 y}{12} > 1 - 6 y$

Step 1

Multiply both sides by $12$ .

$\frac{5 - 2 y}{12} \cdot 12 > (1 - 6 y) \cdot 12$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{5 - 2 y}{12} \cdot 12$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{5 - 2 y}{12} \cdot 12 > (1 - 6 y) \cdot 12$

Rewrite the expression.

$5 - 2 y > (1 - 6 y) \cdot 12$

Reorder $5$ and $- 2 y$ .

$- 2 y + 5 > (1 - 6 y) \cdot 12$

Simplify the right side.

Simplify $(1 - 6 y) \cdot 12$ .

Apply the distributive property.

$- 2 y + 5 > 1 \cdot 12 - 6 y \cdot 12$

Simplify the expression.

Multiply $12$ by $1$ .

$- 2 y + 5 > 12 - 6 y \cdot 12$

Multiply $12$ by $- 6$ .

$- 2 y + 5 > 12 - 72 y$

Reorder $12$ and $- 72 y$ .

$- 2 y + 5 > - 72 y + 12$

Step 3

Solve for $y$ .

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

Add $72 y$ to both sides of the inequality.

$- 2 y + 5 + 72 y > 12$

Add $- 2 y$ and $72 y$ .

$70 y + 5 > 12$

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

Subtract $5$ from both sides of the inequality.

$70 y > 12 - 5$

Subtract $5$ from $12$ .

$70 y > 7$

Divide each term in $70 y > 7$ by $70$ and simplify.

Divide each term in $70 y > 7$ by $70$ .

$\frac{70 y}{70} > \frac{7}{70}$

Simplify the left side.

Cancel the common factor of $70$ .

Cancel the common factor.

$\frac{70 y}{70} > \frac{7}{70}$

Divide $y$ by $1$ .

$y > \frac{7}{70}$

Simplify the right side.

Cancel the common factor of $7$ and $70$ .

Factor $7$ out of $7$ .

$y > \frac{7 (1)}{70}$

Cancel the common factors.

Factor $7$ out of $70$ .

$y > \frac{7 \cdot 1}{7 \cdot 10}$

Cancel the common factor.

$y > \frac{7 \cdot 1}{7 \cdot 10}$

Rewrite the expression.

$y > \frac{1}{10}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y > \frac{1}{10}$

Interval Notation:

$(\frac{1}{10}, \infty)$

Solve the Inequality for y (5-2y)/12>1-6y

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