Solve for x -1/5x-4>-3

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

Step 1

Combine $x$ and $\frac{1}{5}$ .

$- \frac{x}{5} - 4 > - 3$

Step 2

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

Add $4$ to both sides of the inequality.

$- \frac{x}{5} > - 3 + 4$

Add $- 3$ and $4$ .

$- \frac{x}{5} > 1$

Step 3

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

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

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

Simplify the right side.

Divide $1$ by $- 1$ .

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

Step 4

Multiply both sides by $5$ .

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

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$x < - 1 \cdot 5$

Simplify the right side.

Multiply $- 1$ by $5$ .

$x < - 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < - 5$

Interval Notation:

$(- \infty, - 5)$

Solve for x -1/5x-4>-3

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