Algebra Examples

$\frac{1}{4} x + 3 \geq - \frac{3}{4} x + 11$

Step 1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + 3 \geq - \frac{3}{4} x + 11$

Step 2

Simplify each term.

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Step 2.1

Combine $x$ and $\frac{3}{4}$ .

$\frac{x}{4} + 3 \geq - \frac{x \cdot 3}{4} + 11$

Step 2.2

Move $3$ to the left of $x$ .

$\frac{x}{4} + 3 \geq - \frac{3 x}{4} + 11$

Step 3

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

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Step 3.1

Add $\frac{3 x}{4}$ to both sides of the inequality.

$\frac{x}{4} + 3 + \frac{3 x}{4} \geq 11$

Step 3.2

Combine the numerators over the common denominator.

$3 + \frac{x + 3 x}{4} \geq 11$

Step 3.3

Add $x$ and $3 x$ .

$3 + \frac{4 x}{4} \geq 11$

Step 3.4

Cancel the common factor of $4$ .

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Step 3.4.1

Cancel the common factor.

$3 + \frac{4 x}{4} \geq 11$

Step 3.4.2

Divide $x$ by $1$ .

$3 + x \geq 11$

Step 4

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

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Step 4.1

Subtract $3$ from both sides of the inequality.

$x \geq 11 - 3$

Step 4.2

Subtract $3$ from $11$ .

$x \geq 8$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq 8$

Interval Notation:

$[8, \infty)$