Solve for x 2/3x-1

$\frac{2}{3} x - 1 < \frac{4}{5} x + 3$

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

$\frac{2 x}{3} - 1 < \frac{4}{5} x + 3$

Combine $\frac{4}{5}$ and $x$ .

$\frac{2 x}{3} - 1 < \frac{4 x}{5} + 3$

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

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Subtract $\frac{4 x}{5}$ from both sides of the inequality.

$\frac{2 x}{3} - 1 - \frac{4 x}{5} < 3$

To write $\frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 x}{3} \cdot \frac{5}{5} - \frac{4 x}{5} - 1 < 3$

To write $- \frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 x}{3} \cdot \frac{5}{5} - \frac{4 x}{5} \cdot \frac{3}{3} - 1 < 3$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{2 x}{3}$ and $\frac{5}{5}$ .

$\frac{2 x \cdot 5}{3 \cdot 5} - \frac{4 x}{5} \cdot \frac{3}{3} - 1 < 3$

Multiply $3$ by $5$ .

$\frac{2 x \cdot 5}{15} - \frac{4 x}{5} \cdot \frac{3}{3} - 1 < 3$

Multiply $\frac{4 x}{5}$ and $\frac{3}{3}$ .

$\frac{2 x \cdot 5}{15} - \frac{4 x \cdot 3}{5 \cdot 3} - 1 < 3$

Multiply $5$ by $3$ .

$\frac{2 x \cdot 5}{15} - \frac{4 x \cdot 3}{15} - 1 < 3$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 5 - 4 x \cdot 3}{15} - 1 < 3$

Simplify each term.

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Simplify the numerator.

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Factor $2 x$ out of $2 x \cdot 5 - 4 x \cdot 3$ .

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Factor $2 x$ out of $2 x \cdot 5$ .

$\frac{2 x (5) - 4 x \cdot 3}{15} - 1 < 3$

Factor $2 x$ out of $- 4 x \cdot 3$ .

$\frac{2 x (5) + 2 x (- 2 \cdot 3)}{15} - 1 < 3$

Factor $2 x$ out of $2 x (5) + 2 x (- 2 \cdot 3)$ .

$\frac{2 x (5 - 2 \cdot 3)}{15} - 1 < 3$

Multiply $- 2$ by $3$ .

$\frac{2 x (5 - 6)}{15} - 1 < 3$

Subtract $6$ from $5$ .

$\frac{2 x \cdot - 1}{15} - 1 < 3$

Multiply $- 1$ by $2$ .

$\frac{- 2 x}{15} - 1 < 3$

Move the negative in front of the fraction.

$- \frac{2 x}{15} - 1 < 3$

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

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Add $1$ to both sides of the inequality.

$- \frac{2 x}{15} < 3 + 1$

Add $3$ and $1$ .

$- \frac{2 x}{15} < 4$

Multiply each term in $- \frac{2 x}{15} < 4$ by $- 1$

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Multiply each term in $- \frac{2 x}{15} < 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{2 x}{15} \cdot - 1 > 4 \cdot - 1$

Multiply $- \frac{2 x}{15} \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$1 \frac{2 x}{15} > 4 \cdot - 1$

Multiply $\frac{2 x}{15}$ by $1$ .

$\frac{2 x}{15} > 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$\frac{2 x}{15} > - 4$

Multiply both sides of the equation by $15$ .

$2 x > - 4 \cdot 15$

Multiply $- 4$ by $15$ .

$2 x > - 60$

Divide each term by $2$ and simplify.

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Divide each term in $2 x > - 60$ by $2$ .

$\frac{2 x}{2} > \frac{- 60}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 x}{2} > \frac{- 60}{2}$

Divide $x$ by $1$ .

$x > \frac{- 60}{2}$

Divide $- 60$ by $2$ .

$x > - 30$

The result can be shown in multiple forms.

Inequality Form:

$x > - 30$

Interval Notation:

$(- 30, \infty)$

Solve for x 2/3x-1<4/5x+3

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