Solve the Inequality for x (4x)/5+3>x+5

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

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

Subtract $x$ from both sides of the inequality.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

Factor $x$ out of $4 x$ .

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

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

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

Factor $x$ out of $x \cdot 4 + x (- 1 \cdot 5)$ .

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

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $4$ .

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

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

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

Move the negative in front of the fraction.

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

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

Subtract $3$ from both sides of the inequality.

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

Subtract $3$ from $5$ .

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

Divide each term in $- \frac{x}{5} > 2$ by $- 1$ and simplify.

Divide each term in $- \frac{x}{5} > 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

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

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

Simplify the right side.

Divide $2$ by $- 1$ .

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

Multiply both sides by $5$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Rewrite the expression.

$x < - 2 \cdot 5$

Simplify the right side.

Multiply $- 2$ by $5$ .

$x < - 10$

The result can be shown in multiple forms.

Inequality Form:

$x < - 10$

Interval Notation:

$(- \infty, - 10)$

Solve the Inequality for x (4x)/5+3>x+5

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