Algebra Examples

$7 x + \frac{2}{3} > 8 - \frac{1}{4} x$

Step 1

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

$7 x + \frac{2}{3} > 8 - \frac{x}{4}$

Step 2

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

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Step 2.1

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

$7 x + \frac{2}{3} + \frac{x}{4} > 8$

Step 2.2

To write $7 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$7 x \cdot \frac{4}{4} + \frac{x}{4} + \frac{2}{3} > 8$

Step 2.3

Combine $7 x$ and $\frac{4}{4}$ .

$\frac{7 x \cdot 4}{4} + \frac{x}{4} + \frac{2}{3} > 8$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 x \cdot 4 + x}{4} + \frac{2}{3} > 8$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $x$ out of $7 x \cdot 4 + x$ .

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Step 2.5.1.1.1

Factor $x$ out of $7 x \cdot 4$ .

$\frac{x (7 \cdot 4) + x}{4} + \frac{2}{3} > 8$

Step 2.5.1.1.2

Raise $x$ to the power of $1$ .

$\frac{x (7 \cdot 4) + x^{1}}{4} + \frac{2}{3} > 8$

Step 2.5.1.1.3

Factor $x$ out of $x^{1}$ .

$\frac{x (7 \cdot 4) + x \cdot 1}{4} + \frac{2}{3} > 8$

Step 2.5.1.1.4

Factor $x$ out of $x (7 \cdot 4) + x \cdot 1$ .

$\frac{x (7 \cdot 4 + 1)}{4} + \frac{2}{3} > 8$

Step 2.5.1.2

Multiply $7$ by $4$ .

$\frac{x (28 + 1)}{4} + \frac{2}{3} > 8$

Step 2.5.1.3

Add $28$ and $1$ .

$\frac{x \cdot 29}{4} + \frac{2}{3} > 8$

Step 2.5.2

Move $29$ to the left of $x$ .

$\frac{29 x}{4} + \frac{2}{3} > 8$

Step 3

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

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Step 3.1

Subtract $\frac{2}{3}$ from both sides of the inequality.

$\frac{29 x}{4} > 8 - \frac{2}{3}$

Step 3.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{29 x}{4} > 8 \cdot \frac{3}{3} - \frac{2}{3}$

Step 3.3

Combine $8$ and $\frac{3}{3}$ .

$\frac{29 x}{4} > \frac{8 \cdot 3}{3} - \frac{2}{3}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{29 x}{4} > \frac{8 \cdot 3 - 2}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $8$ by $3$ .

$\frac{29 x}{4} > \frac{24 - 2}{3}$

Step 3.5.2

Subtract $2$ from $24$ .

$\frac{29 x}{4} > \frac{22}{3}$

Step 4

Multiply both sides by $4$ .

$\frac{29 x}{4} \cdot 4 > \frac{22}{3} \cdot 4$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{29 x}{4} \cdot 4 > \frac{22}{3} \cdot 4$

Step 5.1.1.2

Rewrite the expression.

$29 x > \frac{22}{3} \cdot 4$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{22}{3} \cdot 4$ .

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Step 5.2.1.1

Combine $\frac{22}{3}$ and $4$ .

$29 x > \frac{22 \cdot 4}{3}$

Step 5.2.1.2

Multiply $22$ by $4$ .

$29 x > \frac{88}{3}$

Step 6

Divide each term in $29 x > \frac{88}{3}$ by $29$ and simplify.

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Step 6.1

Divide each term in $29 x > \frac{88}{3}$ by $29$ .

$\frac{29 x}{29} > \frac{\frac{88}{3}}{29}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $29$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{29 x}{29} > \frac{\frac{88}{3}}{29}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x > \frac{\frac{88}{3}}{29}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$x > \frac{88}{3} \cdot \frac{1}{29}$

Step 6.3.2

Multiply $\frac{88}{3} \cdot \frac{1}{29}$ .

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Step 6.3.2.1

Multiply $\frac{88}{3}$ by $\frac{1}{29}$ .

$x > \frac{88}{3 \cdot 29}$

Step 6.3.2.2

Multiply $3$ by $29$ .

$x > \frac{88}{87}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{88}{87}$

Interval Notation:

$(\frac{88}{87}, \infty)$