Solve the Inequality for x x+4-x/3<(2x)/3

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

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

Simplify the left side.

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

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

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

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

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

Combine the numerators over the common denominator.

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

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

Reorder $x$ and $3$ .

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

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

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

Apply the distributive property.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $4$ by $3$ .

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

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$2 x + 12 < 2 x$

Step 3

Solve for $x$ .

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

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

$2 x + 12 - 2 x < 0$

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

Subtract $2 x$ from $2 x$ .

$0 + 12 < 0$

Add $0$ and $12$ .

$12 < 0$

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

No solution

Solve the Inequality for x x+4-x/3<(2x)/3

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