Solve the Inequality for x (2x-1)/3<1-(x-2)/5

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

Multiply both sides by $3$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $(1 - \frac{x - 2}{5}) \cdot 3$ .

Combine into one fraction.

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $- 1$ by $- 2$ .

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

Add $5$ and $2$ .

$2 x - 1 < \frac{- x + 7}{5} \cdot 3$

Simplify terms.

Combine $\frac{- x + 7}{5}$ and $3$ .

$2 x - 1 < \frac{(- x + 7) \cdot 3}{5}$

Move $3$ to the left of $- x + 7$ .

$2 x - 1 < \frac{3 \cdot (- x + 7)}{5}$

Factor $- 1$ out of $- x$ .

$2 x - 1 < \frac{3 (- (x) + 7)}{5}$

Rewrite $7$ as $- 1 (- 7)$ .

$2 x - 1 < \frac{3 (- (x) - 1 (- 7))}{5}$

Factor $- 1$ out of $- (x) - 1 (- 7)$ .

$2 x - 1 < \frac{3 (- (x - 7))}{5}$

Simplify the expression.

Rewrite $- (x - 7)$ as $- 1 (x - 7)$ .

$2 x - 1 < \frac{3 (- 1 (x - 7))}{5}$

Move the negative in front of the fraction.

$2 x - 1 < - \frac{3 (x - 7)}{5}$

Solve for $x$ .

Multiply both sides by $5$ .

$(2 x - 1) \cdot 5 < - \frac{3 (x - 7)}{5} \cdot 5$

Simplify.

Simplify the left side.

Simplify $(2 x - 1) \cdot 5$ .

Apply the distributive property.

$2 x \cdot 5 - 1 \cdot 5 < - \frac{3 (x - 7)}{5} \cdot 5$

Multiply.

Multiply $5$ by $2$ .

$10 x - 1 \cdot 5 < - \frac{3 (x - 7)}{5} \cdot 5$

Multiply $- 1$ by $5$ .

$10 x - 5 < - \frac{3 (x - 7)}{5} \cdot 5$

Simplify the right side.

Simplify $- \frac{3 (x - 7)}{5} \cdot 5$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{3 (x - 7)}{5}$ into the numerator.

$10 x - 5 < \frac{- 3 (x - 7)}{5} \cdot 5$

Cancel the common factor.

$10 x - 5 < \frac{- 3 (x - 7)}{5} \cdot 5$

Rewrite the expression.

$10 x - 5 < - 3 (x - 7)$

Apply the distributive property.

$10 x - 5 < - 3 x - 3 \cdot - 7$

Multiply $- 3$ by $- 7$ .

$10 x - 5 < - 3 x + 21$

Solve for $x$ .

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

Add $3 x$ to both sides of the inequality.

$10 x - 5 + 3 x < 21$

Add $10 x$ and $3 x$ .

$13 x - 5 < 21$

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

Add $5$ to both sides of the inequality.

$13 x < 21 + 5$

Add $21$ and $5$ .

$13 x < 26$

Divide each term in $13 x < 26$ by $13$ and simplify.

Divide each term in $13 x < 26$ by $13$ .

$\frac{13 x}{13} < \frac{26}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} < \frac{26}{13}$

Divide $x$ by $1$ .

$x < \frac{26}{13}$

Simplify the right side.

Divide $26$ by $13$ .

$x < 2$

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$

Solve the Inequality for x (2x-1)/3<1-(x-2)/5

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