Solve for x 4/5x-1<5/6x+2

$\frac{4}{5} x - 1 < \frac{5}{6} x + 2$

Step 1

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

$\frac{4 x}{5} - 1 < \frac{5}{6} x + 2$

Step 2

Combine $\frac{5}{6}$ and $x$ .

$\frac{4 x}{5} - 1 < \frac{5 x}{6} + 2$

Step 3

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

Subtract $\frac{5 x}{6}$ from both sides of the inequality.

$\frac{4 x}{5} - 1 - \frac{5 x}{6} < 2$

To write $\frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{4 x}{5} \cdot \frac{6}{6} - \frac{5 x}{6} - 1 < 2$

To write $- \frac{5 x}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 x}{5} \cdot \frac{6}{6} - \frac{5 x}{6} \cdot \frac{5}{5} - 1 < 2$

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 x}{5}$ by $\frac{6}{6}$ .

$\frac{4 x \cdot 6}{5 \cdot 6} - \frac{5 x}{6} \cdot \frac{5}{5} - 1 < 2$

Multiply $5$ by $6$ .

$\frac{4 x \cdot 6}{30} - \frac{5 x}{6} \cdot \frac{5}{5} - 1 < 2$

Multiply $\frac{5 x}{6}$ by $\frac{5}{5}$ .

$\frac{4 x \cdot 6}{30} - \frac{5 x \cdot 5}{6 \cdot 5} - 1 < 2$

Multiply $6$ by $5$ .

$\frac{4 x \cdot 6}{30} - \frac{5 x \cdot 5}{30} - 1 < 2$

Combine the numerators over the common denominator.

$\frac{4 x \cdot 6 - 5 x \cdot 5}{30} - 1 < 2$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $4 x \cdot 6 - 5 x \cdot 5$ .

Factor $x$ out of $4 x \cdot 6$ .

$\frac{x (4 \cdot 6) - 5 x \cdot 5}{30} - 1 < 2$

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

$\frac{x (4 \cdot 6) + x (- 5 \cdot 5)}{30} - 1 < 2$

Factor $x$ out of $x (4 \cdot 6) + x (- 5 \cdot 5)$ .

$\frac{x (4 \cdot 6 - 5 \cdot 5)}{30} - 1 < 2$

Multiply $4$ by $6$ .

$\frac{x (24 - 5 \cdot 5)}{30} - 1 < 2$

Multiply $- 5$ by $5$ .

$\frac{x (24 - 25)}{30} - 1 < 2$

Subtract $25$ from $24$ .

$\frac{x \cdot - 1}{30} - 1 < 2$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{30} - 1 < 2$

Move the negative in front of the fraction.

$- \frac{x}{30} - 1 < 2$

Step 4

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

Add $1$ to both sides of the inequality.

$- \frac{x}{30} < 2 + 1$

Add $2$ and $1$ .

$- \frac{x}{30} < 3$

Step 5

Divide each term in $- \frac{x}{30} < 3$ by $- 1$ and simplify.

Divide each term in $- \frac{x}{30} < 3$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{30}}{- 1} > \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{x}{30}}{1} > \frac{3}{- 1}$

Divide $\frac{x}{30}$ by $1$ .

$\frac{x}{30} > \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$\frac{x}{30} > - 3$

Step 6

Multiply both sides by $30$ .

$\frac{x}{30} \cdot 30 > - 3 \cdot 30$

Step 7

Simplify.

Simplify the left side.

Cancel the common factor of $30$ .

Cancel the common factor.

$\frac{x}{30} \cdot 30 > - 3 \cdot 30$

Rewrite the expression.

$x > - 3 \cdot 30$

Simplify the right side.

Multiply $- 3$ by $30$ .

$x > - 90$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$x > - 90$

Interval Notation:

$(- 90, \infty)$

Solve for x 4/5x-1<5/6x+2

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