Pre-Algebra Examples

$\frac{6}{7} x < 6$

Step 1

Multiply each term in $\frac{6}{7} x < 6$ by $\frac{7}{6}$ .

$\frac{6}{7} x \frac{7}{6} < 6 (\frac{7}{6})$

Step 2

Simplify the left side.

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Step 2.1

Combine $\frac{6}{7}$ and $x$ .

$\frac{6 x}{7} \cdot \frac{7}{6} < 6 (\frac{7}{6})$

Step 2.2

Cancel the common factor of $6$ .

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Step 2.2.1

Factor $6$ out of $6 x$ .

$\frac{6 (x)}{7} \cdot \frac{7}{6} < 6 (\frac{7}{6})$

Step 2.2.2

Cancel the common factor.

$\frac{6 x}{7} \cdot \frac{7}{6} < 6 (\frac{7}{6})$

Step 2.2.3

Rewrite the expression.

$\frac{x}{7} \cdot 7 < 6 (\frac{7}{6})$

Step 2.3

Cancel the common factor of $7$ .

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Step 2.3.1

Cancel the common factor.

$\frac{x}{7} \cdot 7 < 6 (\frac{7}{6})$

Step 2.3.2

Rewrite the expression.

$x < 6 (\frac{7}{6})$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $6$ .

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Step 3.1.1

Cancel the common factor.

$x < 6 (\frac{7}{6})$

Step 3.1.2

Rewrite the expression.

$x < 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 7$

Interval Notation:

$(- \infty, 7)$