Solve the System of Inequalities -1.2<1-2y<2.4

$- 1.2 < 1 - 2 y < 2.4$

Solve $- 1.2 < 1 - 2 y$ for $y$ .

Rewrite so $y$ is on the left side of the inequality.

$1 - 2 y > - 1.2$

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

Subtract $1$ from both sides of the inequality.

$- 2 y > - 1.2 - 1$

Subtract $1$ from $- 1.2$ .

$- 2 y > - 2.2$

Divide each term in $- 2 y > - 2.2$ by $- 2$ and simplify.

Divide each term in $- 2 y > - 2.2$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} < \frac{- 2.2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} < \frac{- 2.2}{- 2}$

Divide $y$ by $1$ .

$y < \frac{- 2.2}{- 2}$

Simplify the right side.

Divide $- 2.2$ by $- 2$ .

$y < 1.1$

Solve $1 - 2 y < 2.4$ for $y$ .

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

Subtract $1$ from both sides of the inequality.

$- 2 y < 2.4 - 1$

Subtract $1$ from $2.4$ .

$- 2 y < 1.4$

Divide each term in $- 2 y < 1.4$ by $- 2$ and simplify.

Divide each term in $- 2 y < 1.4$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 y}{- 2} > \frac{1.4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} > \frac{1.4}{- 2}$

Divide $y$ by $1$ .

$y > \frac{1.4}{- 2}$

Simplify the right side.

Divide $1.4$ by $- 2$ .

$y > - 0.7$

Find the intersection of $y < 1.1$ and $y > - 0.7$ .

$- 0.7 < y < 1.1$

The result can be shown in multiple forms.

Inequality Form:

$- 0.7 < y < 1.1$

Interval Notation:

$(- 0.7, 1.1)$

Solve the System of Inequalities -1.2<1-2y<2.4

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