Solve the System of Inequalities 4x+2>10 and -3x-1>5

$4 x + 2 > 10$ and $- 3 x - 1 > 5$

Simplify the first inequality.

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

Subtract $2$ from both sides of the inequality.

$4 x > 10 - 2$ and $- 3 x - 1 > 5$

Subtract $2$ from $10$ .

$4 x > 8$ and $- 3 x - 1 > 5$

Divide each term in $4 x > 8$ by $4$ and simplify.

Divide each term in $4 x > 8$ by $4$ .

$\frac{4 x}{4} > \frac{8}{4}$ and $- 3 x - 1 > 5$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{8}{4}$ and $- 3 x - 1 > 5$

Divide $x$ by $1$ .

$x > \frac{8}{4}$ and $- 3 x - 1 > 5$

Simplify the right side.

Divide $8$ by $4$ .

$x > 2$ and $- 3 x - 1 > 5$

Simplify the second inequality.

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

Add $1$ to both sides of the inequality.

$x > 2$ and $- 3 x > 5 + 1$

Add $5$ and $1$ .

$x > 2$ and $- 3 x > 6$

Divide each term in $- 3 x > 6$ by $- 3$ and simplify.

Divide each term in $- 3 x > 6$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x > 2$ and $\frac{- 3 x}{- 3} < \frac{6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$x > 2$ and $\frac{- 3 x}{- 3} < \frac{6}{- 3}$

Divide $x$ by $1$ .

$x > 2$ and $x < \frac{6}{- 3}$

Simplify the right side.

Divide $6$ by $- 3$ .

$x > 2$ and $x < - 2$

The intersection consists of the elements that are contained in both intervals.

No solution

Solve the System of Inequalities 4x+2>10 and -3x-1>5

Related Questions

Support LCMGCF.com by disabling your adblocker.