Solve the Inequality for y 7>=-3/2y+1

$7 \geq - \frac{3}{2} y + 1$

Step 1

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

$- \frac{3}{2} y + 1 \leq 7$

Step 2

Simplify each term.

Combine $y$ and $\frac{3}{2}$ .

$- \frac{y \cdot 3}{2} + 1 \leq 7$

Move $3$ to the left of $y$ .

$- \frac{3 y}{2} + 1 \leq 7$

Step 3

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

Subtract $1$ from both sides of the inequality.

$- \frac{3 y}{2} \leq 7 - 1$

Subtract $1$ from $7$ .

$- \frac{3 y}{2} \leq 6$

Step 4

Divide each term in $- \frac{3 y}{2} \leq 6$ by $- 1$ and simplify.

Divide each term in $- \frac{3 y}{2} \leq 6$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 y}{2}}{- 1} \geq \frac{6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{3 y}{2}}{1} \geq \frac{6}{- 1}$

Divide $\frac{3 y}{2}$ by $1$ .

$\frac{3 y}{2} \geq \frac{6}{- 1}$

Simplify the right side.

Divide $6$ by $- 1$ .

$\frac{3 y}{2} \geq - 6$

Step 5

Multiply both sides by $2$ .

$\frac{3 y}{2} \cdot 2 \geq - 6 \cdot 2$

Step 6

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 y}{2} \cdot 2 \geq - 6 \cdot 2$

Rewrite the expression.

$3 y \geq - 6 \cdot 2$

Simplify the right side.

Multiply $- 6$ by $2$ .

$3 y \geq - 12$

Step 7

Divide each term in $3 y \geq - 12$ by $3$ and simplify.

Divide each term in $3 y \geq - 12$ by $3$ .

$\frac{3 y}{3} \geq \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} \geq \frac{- 12}{3}$

Divide $y$ by $1$ .

$y \geq \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$y \geq - 4$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$y \geq - 4$

Interval Notation:

$[- 4, \infty)$

Solve the Inequality for y 7>=-3/2y+1

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