Solve the System of Inequalities 8x+15<=4x-5 and -7x+2<-6x+3

$8 x + 15 \leq 4 x - 5$ and $- 7 x + 2 < - 6 x + 3$

Step 1

Simplify the first inequality.

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

Subtract $4 x$ from both sides of the inequality.

$8 x + 15 - 4 x \leq - 5$ and $- 7 x + 2 < - 6 x + 3$

Subtract $4 x$ from $8 x$ .

$4 x + 15 \leq - 5$ and $- 7 x + 2 < - 6 x + 3$

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

Subtract $15$ from both sides of the inequality.

$4 x \leq - 5 - 15$ and $- 7 x + 2 < - 6 x + 3$

Subtract $15$ from $- 5$ .

$4 x \leq - 20$ and $- 7 x + 2 < - 6 x + 3$

Divide each term in $4 x \leq - 20$ by $4$ and simplify.

Divide each term in $4 x \leq - 20$ by $4$ .

$\frac{4 x}{4} \leq \frac{- 20}{4}$ and $- 7 x + 2 < - 6 x + 3$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \leq \frac{- 20}{4}$ and $- 7 x + 2 < - 6 x + 3$

Divide $x$ by $1$ .

$x \leq \frac{- 20}{4}$ and $- 7 x + 2 < - 6 x + 3$

Simplify the right side.

Divide $- 20$ by $4$ .

$x \leq - 5$ and $- 7 x + 2 < - 6 x + 3$

Step 2

Simplify the second inequality.

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

Add $6 x$ to both sides of the inequality.

$x \leq - 5$ and $- 7 x + 2 + 6 x < 3$

Add $- 7 x$ and $6 x$ .

$x \leq - 5$ and $- x + 2 < 3$

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

Subtract $2$ from both sides of the inequality.

$x \leq - 5$ and $- x < 3 - 2$

Subtract $2$ from $3$ .

$x \leq - 5$ and $- x < 1$

Divide each term in $- x < 1$ by $- 1$ and simplify.

Divide each term in $- x < 1$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x \leq - 5$ and $\frac{- x}{- 1} > \frac{1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$x \leq - 5$ and $\frac{x}{1} > \frac{1}{- 1}$

Divide $x$ by $1$ .

$x \leq - 5$ and $x > \frac{1}{- 1}$

Simplify the right side.

Divide $1$ by $- 1$ .

$x \leq - 5$ and $x > - 1$

Step 3

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

No solution

Solve the System of Inequalities 8x+15<=4x-5 and -7x+2<-6x+3

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