Algebra Examples

$x - 1 \leq 2 x - 3 \leq 3 x - 5$

Step 1

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

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Step 1.1

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

$x - 1 - 2 x \leq - 3$

Step 1.2

Subtract $2 x$ from $x$ .

$- x - 1 \leq - 3$

Step 2

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

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Step 2.1

Add $1$ to both sides of the inequality.

$- x \leq - 3 + 1$

Step 2.2

Add $- 3$ and $1$ .

$- x \leq - 2$

Step 3

Divide each term in $- x \leq - 2$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x \leq - 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{- 2}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{- 2}{- 1}$

Step 3.2.2

Divide $x$ by $1$ .

$x \geq \frac{- 2}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 2$ by $- 1$ .

$x \geq 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 2$

Interval Notation:

$[2, \infty)$

Step 5