Solve the Inequality for x -2(3/5x+6)-1>4x

$- 2 (\frac{3}{5} x + 6) - 1 > 4 x$

Step 1

Simplify $- 2 (\frac{3}{5} x + 6) - 1$ .

Simplify each term.

Combine $\frac{3}{5}$ and $x$ .

$- 2 (\frac{3 x}{5} + 6) - 1 > 4 x$

Apply the distributive property.

$- 2 \frac{3 x}{5} - 2 \cdot 6 - 1 > 4 x$

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

Combine $- 2$ and $\frac{3 x}{5}$ .

$\frac{- 2 (3 x)}{5} - 2 \cdot 6 - 1 > 4 x$

Multiply $3$ by $- 2$ .

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

Multiply $- 2$ by $6$ .

$\frac{- 6 x}{5} - 12 - 1 > 4 x$

Move the negative in front of the fraction.

$- \frac{6 x}{5} - 12 - 1 > 4 x$

Subtract $1$ from $- 12$ .

$- \frac{6 x}{5} - 13 > 4 x$

Step 2

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

Subtract $4 x$ from both sides of the inequality.

$- \frac{6 x}{5} - 13 - 4 x > 0$

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

$- \frac{6 x}{5} - 4 x \cdot \frac{5}{5} - 13 > 0$

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

$- \frac{6 x}{5} + \frac{- 4 x \cdot 5}{5} - 13 > 0$

Combine the numerators over the common denominator.

$\frac{- 6 x - 4 x \cdot 5}{5} - 13 > 0$

Simplify each term.

Simplify the numerator.

Factor $2 x$ out of $- 6 x - 4 x \cdot 5$ .

Factor $2 x$ out of $- 6 x$ .

$\frac{2 x (- 3) - 4 x \cdot 5}{5} - 13 > 0$

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

$\frac{2 x (- 3) + 2 x (- 2 \cdot 5)}{5} - 13 > 0$

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

$\frac{2 x (- 3 - 2 \cdot 5)}{5} - 13 > 0$

Multiply $- 2$ by $5$ .

$\frac{2 x (- 3 - 10)}{5} - 13 > 0$

Subtract $10$ from $- 3$ .

$\frac{2 x \cdot - 13}{5} - 13 > 0$

Multiply $- 13$ by $2$ .

$\frac{- 26 x}{5} - 13 > 0$

Move the negative in front of the fraction.

$- \frac{26 x}{5} - 13 > 0$

Step 3

Add $13$ to both sides of the inequality.

$- \frac{26 x}{5} > 13$

Step 4

Divide each term in $- \frac{26 x}{5} > 13$ by $- 1$ and simplify.

Divide each term in $- \frac{26 x}{5} > 13$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{26 x}{5}}{- 1} < \frac{13}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{26 x}{5}}{1} < \frac{13}{- 1}$

Divide $\frac{26 x}{5}$ by $1$ .

$\frac{26 x}{5} < \frac{13}{- 1}$

Simplify the right side.

Divide $13$ by $- 1$ .

$\frac{26 x}{5} < - 13$

Step 5

Multiply both sides by $5$ .

$\frac{26 x}{5} \cdot 5 < - 13 \cdot 5$

Step 6

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{26 x}{5} \cdot 5 < - 13 \cdot 5$

Rewrite the expression.

$26 x < - 13 \cdot 5$

Simplify the right side.

Multiply $- 13$ by $5$ .

$26 x < - 65$

Step 7

Divide each term in $26 x < - 65$ by $26$ and simplify.

Divide each term in $26 x < - 65$ by $26$ .

$\frac{26 x}{26} < \frac{- 65}{26}$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 x}{26} < \frac{- 65}{26}$

Divide $x$ by $1$ .

$x < \frac{- 65}{26}$

Simplify the right side.

Cancel the common factor of $- 65$ and $26$ .

Factor $13$ out of $- 65$ .

$x < \frac{13 (- 5)}{26}$

Cancel the common factors.

Factor $13$ out of $26$ .

$x < \frac{13 \cdot - 5}{13 \cdot 2}$

Cancel the common factor.

$x < \frac{13 \cdot - 5}{13 \cdot 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 8

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(- \infty, - \frac{5}{2})$

Solve the Inequality for x -2(3/5x+6)-1>4x

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