Algebra Examples

$x + 4 - \frac{x}{3} < \frac{2 x}{3}$

Step 1

Multiply both sides by $3$ .

$(x + 4 - \frac{x}{3}) \cdot 3 < \frac{2 x}{3} \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(x + 4 - \frac{x}{3}) \cdot 3$ .

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Step 2.1.1.1

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

$(x \cdot \frac{3}{3} - \frac{x}{3} + 4) \cdot 3 < \frac{2 x}{3} \cdot 3$

Step 2.1.1.2

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

$(\frac{x \cdot 3}{3} - \frac{x}{3} + 4) \cdot 3 < \frac{2 x}{3} \cdot 3$

Step 2.1.1.3

Combine the numerators over the common denominator.

$(\frac{x \cdot 3 - x}{3} + 4) \cdot 3 < \frac{2 x}{3} \cdot 3$

Step 2.1.1.4

Subtract $x$ from $x \cdot 3$ .

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Step 2.1.1.4.1

Reorder $x$ and $3$ .

$(\frac{3 \cdot x - x}{3} + 4) \cdot 3 < \frac{2 x}{3} \cdot 3$

Step 2.1.1.4.2

Subtract $x$ from $3 \cdot x$ .

$(\frac{2 \cdot x}{3} + 4) \cdot 3 < \frac{2 x}{3} \cdot 3$

Step 2.1.1.5

Apply the distributive property.

$\frac{2 x}{3} \cdot 3 + 4 \cdot 3 < \frac{2 x}{3} \cdot 3$

Step 2.1.1.6

Cancel the common factor of $3$ .

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Step 2.1.1.6.1

Cancel the common factor.

$\frac{2 x}{3} \cdot 3 + 4 \cdot 3 < \frac{2 x}{3} \cdot 3$

Step 2.1.1.6.2

Rewrite the expression.

$2 x + 4 \cdot 3 < \frac{2 x}{3} \cdot 3$

Step 2.1.1.7

Multiply $4$ by $3$ .

$2 x + 12 < \frac{2 x}{3} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$2 x + 12 < \frac{2 x}{3} \cdot 3$

Step 2.2.1.2

Rewrite the expression.

$2 x + 12 < 2 x$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $2 x$ from both sides of the inequality.

$2 x + 12 - 2 x < 0$

Step 3.1.2

Combine the opposite terms in $2 x + 12 - 2 x$ .

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Step 3.1.2.1

Subtract $2 x$ from $2 x$ .

$0 + 12 < 0$

Step 3.1.2.2

Add $0$ and $12$ .

$12 < 0$

Step 3.2

Since $12 > 0$ , there are no solutions.

No solution