Algebra Examples

$9 - x \leq 3 + 2 x$ and $3 x - 7 \leq - 22$

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Subtract $2 x$ from both sides of the inequality.

$9 - x - 2 x \leq 3$

Step 1.1.2

Subtract $2 x$ from $- x$ .

$9 - 3 x \leq 3$

Step 1.2

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

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Step 1.2.1

Subtract $9$ from both sides of the inequality.

$- 3 x \leq 3 - 9$

Step 1.2.2

Subtract $9$ from $3$ .

$- 3 x \leq - 6$

Step 1.3

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

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Step 1.3.1

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

$\frac{- 3 x}{- 3} \geq \frac{- 6}{- 3}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 3$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} \geq \frac{- 6}{- 3}$

Step 1.3.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 6}{- 3}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $- 6$ by $- 3$ .

$x \geq 2$

Step 2

Simplify the second inequality.

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Step 2.1

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

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Step 2.1.1

Add $7$ to both sides of the inequality.

$3 x \leq - 22 + 7$

Step 2.1.2

Add $- 22$ and $7$ .

$3 x \leq - 15$

Step 2.2

Divide each term in $3 x \leq - 15$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x \leq - 15$ by $3$ .

$\frac{3 x}{3} \leq \frac{- 15}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{- 15}{3}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 15}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 15$ by $3$ .

$x \leq - 5$

Step 3

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

No solution