Precalculus Examples

$8 x - 1 > 4 x + 11$

Step 1

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

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Step 1.1

Subtract $4 x$ from both sides of the inequality.

$8 x - 1 - 4 x > 11$

Step 1.2

Subtract $4 x$ from $8 x$ .

$4 x - 1 > 11$

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.

$4 x > 11 + 1$

Step 2.2

Add $11$ and $1$ .

$4 x > 12$

Step 3

Divide each term in $4 x > 12$ by $4$ and simplify.

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Step 3.1

Divide each term in $4 x > 12$ by $4$ .

$\frac{4 x}{4} > \frac{12}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} > \frac{12}{4}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x > \frac{12}{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $12$ by $4$ .

$x > 3$

Step 4

Convert the inequality to interval notation.

$(3, \infty)$

Step 5