Solve the System of Inequalities 4x+15>=-9 and 8x-6<=34

$4 x + 15 \geq - 9$ and $8 x - 6 \leq 34$

Step 1

Simplify the first inequality.

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

Subtract $15$ from both sides of the inequality.

$4 x \geq - 9 - 15$

Subtract $15$ from $- 9$ .

$4 x \geq - 24$

Divide each term in $4 x \geq - 24$ by $4$ and simplify.

Divide each term in $4 x \geq - 24$ by $4$ .

$\frac{4 x}{4} \geq \frac{- 24}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{- 24}{4}$

Divide $x$ by $1$ .

$x \geq \frac{- 24}{4}$

Simplify the right side.

Divide $- 24$ by $4$ .

$x \geq - 6$

Step 2

Simplify the second inequality.

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

Add $6$ to both sides of the inequality.

$8 x \leq 34 + 6$

Add $34$ and $6$ .

$8 x \leq 40$

Divide each term in $8 x \leq 40$ by $8$ and simplify.

Divide each term in $8 x \leq 40$ by $8$ .

$\frac{8 x}{8} \leq \frac{40}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} \leq \frac{40}{8}$

Divide $x$ by $1$ .

$x \leq \frac{40}{8}$

Simplify the right side.

Divide $40$ by $8$ .

$x \leq 5$

Step 3

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

$- 6 \leq x \leq 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 6 \leq x \leq 5$

Interval Notation:

$[- 6, 5]$

Step 5

Solve the System of Inequalities 4x+15>=-9 and 8x-6<=34

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