Solve the System of Inequalities 4x-3>5 and 6x+2<-10

$4 x - 3 > 5$ and $6 x + 2 < - 10$

Step 1

Simplify the first inequality.

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

Add $3$ to both sides of the inequality.

$4 x > 5 + 3$ and $6 x + 2 < - 10$

Add $5$ and $3$ .

$4 x > 8$ and $6 x + 2 < - 10$

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 $6 x + 2 < - 10$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{8}{4}$ and $6 x + 2 < - 10$

Divide $x$ by $1$ .

$x > \frac{8}{4}$ and $6 x + 2 < - 10$

Simplify the right side.

Divide $8$ by $4$ .

$x > 2$ and $6 x + 2 < - 10$

Step 2

Simplify the second inequality.

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

Subtract $2$ from both sides of the inequality.

$x > 2$ and $6 x < - 10 - 2$

Subtract $2$ from $- 10$ .

$x > 2$ and $6 x < - 12$

Divide each term in $6 x < - 12$ by $6$ and simplify.

Divide each term in $6 x < - 12$ by $6$ .

$x > 2$ and $\frac{6 x}{6} < \frac{- 12}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$x > 2$ and $\frac{6 x}{6} < \frac{- 12}{6}$

Divide $x$ by $1$ .

$x > 2$ and $x < \frac{- 12}{6}$

Simplify the right side.

Divide $- 12$ by $6$ .

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

Step 3

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

No solution