Algebra Examples

$9 x + 4 \leq 58$ or $\frac{1}{6} x - 2 > 3$

Step 1

Simplify the first inequality.

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Step 1.1

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

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Step 1.1.1

Subtract $4$ from both sides of the inequality.

$9 x \leq 58 - 4$ or $\frac{1}{6} x - 2 > 3$

Step 1.1.2

Subtract $4$ from $58$ .

$9 x \leq 54$ or $\frac{1}{6} x - 2 > 3$

Step 1.2

Divide each term in $9 x \leq 54$ by $9$ and simplify.

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Step 1.2.1

Divide each term in $9 x \leq 54$ by $9$ .

$\frac{9 x}{9} \leq \frac{54}{9}$ or $\frac{1}{6} x - 2 > 3$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $9$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} \leq \frac{54}{9}$ or $\frac{1}{6} x - 2 > 3$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{54}{9}$ or $\frac{1}{6} x - 2 > 3$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $54$ by $9$ .

$x \leq 6$ or $\frac{1}{6} x - 2 > 3$

Step 2

Simplify the second inequality.

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Step 2.1

Combine $\frac{1}{6}$ and $x$ .

$x \leq 6$ or $\frac{x}{6} - 2 > 3$

Step 2.2

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

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Step 2.2.1

Add $2$ to both sides of the inequality.

$x \leq 6$ or $\frac{x}{6} > 3 + 2$

Step 2.2.2

Add $3$ and $2$ .

$x \leq 6$ or $\frac{x}{6} > 5$

Step 2.3

Multiply both sides by $6$ .

$x \leq 6$ or $\frac{x}{6} \cdot 6 > 5 \cdot 6$

Step 2.4

Simplify.

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Cancel the common factor of $6$ .

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Step 2.4.1.1.1

Cancel the common factor.

$x \leq 6$ or $\frac{x}{6} \cdot 6 > 5 \cdot 6$

Step 2.4.1.1.2

Rewrite the expression.

$x \leq 6$ or $x > 5 \cdot 6$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Multiply $5$ by $6$ .

$x \leq 6$ or $x > 30$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \leq 6 or x > 30$

Interval Notation:

$(- \infty, 6] \cup (30, \infty)$

Step 4