Algebra Examples

$\frac{5 + 6 x}{2} > 3$

Step 1

Multiply both sides by $2$ .

$\frac{5 + 6 x}{2} \cdot 2 > 3 \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{5 + 6 x}{2} \cdot 2$ .

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Step 2.1.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{5 + 6 x}{2} \cdot 2 > 3 \cdot 2$

Step 2.1.1.1.2

Rewrite the expression.

$5 + 6 x > 3 \cdot 2$

$5 + 6 x > 3 \cdot 2$

Step 2.1.1.2

Reorder $5$ and $6 x$ .

$6 x + 5 > 3 \cdot 2$

$6 x + 5 > 3 \cdot 2$

$6 x + 5 > 3 \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3$ by $2$ .

$6 x + 5 > 6$

$6 x + 5 > 6$

$6 x + 5 > 6$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $5$ from both sides of the inequality.

$6 x > 6 - 5$

Step 3.1.2

Subtract $5$ from $6$ .

$6 x > 1$

$6 x > 1$

Step 3.2

Divide each term in $6 x > 1$ by $6$ and simplify.

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Step 3.2.1

Divide each term in $6 x > 1$ by $6$ .

$\frac{6 x}{6} > \frac{1}{6}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} > \frac{1}{6}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{1}{6}$

$x > \frac{1}{6}$

$x > \frac{1}{6}$

$x > \frac{1}{6}$

$x > \frac{1}{6}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{1}{6}$

Interval Notation:

$(\frac{1}{6}, \infty)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$