Algebra Examples

$2 x + y \leq 4 x - 1 \geq 0$

Step 1

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

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Step 1.1

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

$y \leq 4 x - 1 - 2 x$

Step 1.2

Subtract $2 x$ from $4 x$ .

$y \leq 2 x - 1$

Step 2

Solve $4 x - 1 \geq 0$ for $x$ .

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Step 2.1

Add $1$ to both sides of the inequality.

$4 x \geq 1$

Step 2.2

Divide each term in $4 x \geq 1$ by $4$ and simplify.

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Step 2.2.1

Divide each term in $4 x \geq 1$ by $4$ .

$\frac{4 x}{4} \geq \frac{1}{4}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{1}{4}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{1}{4}$

Step 3

Find the intersection of $y \leq 2 x - 1$ and $x \geq \frac{1}{4}$ .

$\frac{1}{4} \leq x \leq 2 x - 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$\frac{1}{4} \leq x \leq 2 x - 1$

Interval Notation:

$[\frac{1}{4}, 2 x - 1]$

Step 5