Solve the System of Inequalities 4a+8>11a+15 and 13-14a<=13-3a

$4 a + 8 > 11 a + 15$ and $13 - 14 a \leq 13 - 3 a$

Step 1

Simplify the first inequality.

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

Subtract $11 a$ from both sides of the inequality.

$4 a + 8 - 11 a > 15$ and $13 - 14 a \leq 13 - 3 a$

Subtract $11 a$ from $4 a$ .

$- 7 a + 8 > 15$ and $13 - 14 a \leq 13 - 3 a$

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

Subtract $8$ from both sides of the inequality.

$- 7 a > 15 - 8$ and $13 - 14 a \leq 13 - 3 a$

Subtract $8$ from $15$ .

$- 7 a > 7$ and $13 - 14 a \leq 13 - 3 a$

Divide each term in $- 7 a > 7$ by $- 7$ and simplify.

Divide each term in $- 7 a > 7$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 a}{- 7} < \frac{7}{- 7}$ and $13 - 14 a \leq 13 - 3 a$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 a}{- 7} < \frac{7}{- 7}$ and $13 - 14 a \leq 13 - 3 a$

Divide $a$ by $1$ .

$a < \frac{7}{- 7}$ and $13 - 14 a \leq 13 - 3 a$

Simplify the right side.

Divide $7$ by $- 7$ .

$a < - 1$ and $13 - 14 a \leq 13 - 3 a$

Step 2

Simplify the second inequality.

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

Add $3 a$ to both sides of the inequality.

$a < - 1$ and $13 - 14 a + 3 a \leq 13$

Add $- 14 a$ and $3 a$ .

$a < - 1$ and $13 - 11 a \leq 13$

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

Subtract $13$ from both sides of the inequality.

$a < - 1$ and $- 11 a \leq 13 - 13$

Subtract $13$ from $13$ .

$a < - 1$ and $- 11 a \leq 0$

Divide each term in $- 11 a \leq 0$ by $- 11$ and simplify.

Divide each term in $- 11 a \leq 0$ by $- 11$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$a < - 1$ and $\frac{- 11 a}{- 11} \geq \frac{0}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$a < - 1$ and $\frac{- 11 a}{- 11} \geq \frac{0}{- 11}$

Divide $a$ by $1$ .

$a < - 1$ and $a \geq \frac{0}{- 11}$

Simplify the right side.

Divide $0$ by $- 11$ .

$a < - 1$ and $a \geq 0$

Step 3

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

No solution

Solve the System of Inequalities 4a+8>11a+15 and 13-14a<=13-3a

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