Solve the Inequality for y 3y-1>-1+6y

$3 y - 1 > - 1 + 6 y$

Step 1

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

Subtract $6 y$ from both sides of the inequality.

$3 y - 1 - 6 y > - 1$

Subtract $6 y$ from $3 y$ .

$- 3 y - 1 > - 1$

Step 2

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

Add $1$ to both sides of the inequality.

$- 3 y > - 1 + 1$

Add $- 1$ and $1$ .

$- 3 y > 0$

Step 3

Divide each term in $- 3 y > 0$ by $- 3$ and simplify.

Divide each term in $- 3 y > 0$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} < \frac{0}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} < \frac{0}{- 3}$

Divide $y$ by $1$ .

$y < \frac{0}{- 3}$

Simplify the right side.

Divide $0$ by $- 3$ .

$y < 0$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y < 0$

Interval Notation:

$(- \infty, 0)$

Solve the Inequality for y 3y-1>-1+6y

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