Algebra Examples

$0.7 x - 2.1 < 0$ $\frac{2}{3} x > 1$

Step 1

Solve $0.7 x - 2.1 < 0$ for $x$ .

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Step 1.1

Add $2.1$ to both sides of the inequality.

$0.7 x < 2.1$

Step 1.2

Divide each term in $0.7 x < 2.1$ by $0.7$ and simplify.

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Step 1.2.1

Divide each term in $0.7 x < 2.1$ by $0.7$ .

$\frac{0.7 x}{0.7} < \frac{2.1}{0.7}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $0.7$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{0.7 x}{0.7} < \frac{2.1}{0.7}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{2.1}{0.7}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $2.1$ by $0.7$ .

$x < 3$

Step 2

Multiply each term in $\frac{2}{3} x > 1$ by $\frac{3}{2}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{2}{3} x > 1$ by $\frac{3}{2}$ .

$\frac{2}{3} x \frac{3}{2} > 1 (\frac{3}{2})$

Step 2.2

Simplify the left side.

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Step 2.2.1

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} \cdot \frac{3}{2} > 1 (\frac{3}{2})$

Step 2.2.2

Cancel the common factor of $2$ .

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Step 2.2.2.1

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{3} \cdot \frac{3}{2} > 1 (\frac{3}{2})$

Step 2.2.2.2

Cancel the common factor.

$\frac{2 x}{3} \cdot \frac{3}{2} > 1 (\frac{3}{2})$

Step 2.2.2.3

Rewrite the expression.

$\frac{x}{3} \cdot 3 > 1 (\frac{3}{2})$

Step 2.2.3

Cancel the common factor of $3$ .

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Step 2.2.3.1

Cancel the common factor.

$\frac{x}{3} \cdot 3 > 1 (\frac{3}{2})$

Step 2.2.3.2

Rewrite the expression.

$x > 1 (\frac{3}{2})$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $\frac{3}{2}$ by $1$ .

$x > \frac{3}{2}$

Step 3

Find the intersection of $x < 3$ and $x > \frac{3}{2}$ .

$\frac{3}{2} < x < 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$\frac{3}{2} < x < 3$

Interval Notation:

$(\frac{3}{2}, 3)$

Step 5