Solve the Inequality for x 5/2x<=6+5(2x+3)

$\frac{5}{2} x \leq 6 + 5 (2 x + 3)$

Step 1

Simplify $\frac{5}{2} x$ .

Rewrite.

$0 + 0 + \frac{5}{2} x \leq 6 + 5 (2 x + 3)$

Simplify by adding zeros.

$\frac{5}{2} x \leq 6 + 5 (2 x + 3)$

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

$\frac{5 x}{2} \leq 6 + 5 (2 x + 3)$

Step 2

Simplify $6 + 5 (2 x + 3)$ .

Simplify each term.

Apply the distributive property.

$\frac{5 x}{2} \leq 6 + 5 (2 x) + 5 \cdot 3$

Multiply $2$ by $5$ .

$\frac{5 x}{2} \leq 6 + 10 x + 5 \cdot 3$

Multiply $5$ by $3$ .

$\frac{5 x}{2} \leq 6 + 10 x + 15$

Add $6$ and $15$ .

$\frac{5 x}{2} \leq 10 x + 21$

Step 3

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

Subtract $10 x$ from both sides of the inequality.

$\frac{5 x}{2} - 10 x \leq 21$

To write $- 10 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{2} - 10 x \cdot \frac{2}{2} \leq 21$

Combine $- 10 x$ and $\frac{2}{2}$ .

$\frac{5 x}{2} + \frac{- 10 x \cdot 2}{2} \leq 21$

Combine the numerators over the common denominator.

$\frac{5 x - 10 x \cdot 2}{2} \leq 21$

Simplify the numerator.

Factor $5 x$ out of $5 x - 10 x \cdot 2$ .

Factor $5 x$ out of $5 x$ .

$\frac{5 x (1) - 10 x \cdot 2}{2} \leq 21$

Factor $5 x$ out of $- 10 x \cdot 2$ .

$\frac{5 x (1) + 5 x (- 2 \cdot 2)}{2} \leq 21$

Factor $5 x$ out of $5 x (1) + 5 x (- 2 \cdot 2)$ .

$\frac{5 x (1 - 2 \cdot 2)}{2} \leq 21$

Multiply $- 2$ by $2$ .

$\frac{5 x (1 - 4)}{2} \leq 21$

Subtract $4$ from $1$ .

$\frac{5 x \cdot - 3}{2} \leq 21$

Multiply $- 3$ by $5$ .

$\frac{- 15 x}{2} \leq 21$

Move the negative in front of the fraction.

$- \frac{15 x}{2} \leq 21$

Step 4

Divide each term in $- \frac{15 x}{2} \leq 21$ by $- 1$ and simplify.

Divide each term in $- \frac{15 x}{2} \leq 21$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{15 x}{2}}{- 1} \geq \frac{21}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{15 x}{2}}{1} \geq \frac{21}{- 1}$

Divide $\frac{15 x}{2}$ by $1$ .

$\frac{15 x}{2} \geq \frac{21}{- 1}$

Simplify the right side.

Divide $21$ by $- 1$ .

$\frac{15 x}{2} \geq - 21$

Step 5

Multiply both sides by $2$ .

$\frac{15 x}{2} \cdot 2 \geq - 21 \cdot 2$

Step 6

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{15 x}{2} \cdot 2 \geq - 21 \cdot 2$

Rewrite the expression.

$15 x \geq - 21 \cdot 2$

Simplify the right side.

Multiply $- 21$ by $2$ .

$15 x \geq - 42$

Step 7

Divide each term in $15 x \geq - 42$ by $15$ and simplify.

Divide each term in $15 x \geq - 42$ by $15$ .

$\frac{15 x}{15} \geq \frac{- 42}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 x}{15} \geq \frac{- 42}{15}$

Divide $x$ by $1$ .

$x \geq \frac{- 42}{15}$

Simplify the right side.

Cancel the common factor of $- 42$ and $15$ .

Factor $3$ out of $- 42$ .

$x \geq \frac{3 (- 14)}{15}$

Cancel the common factors.

Factor $3$ out of $15$ .

$x \geq \frac{3 \cdot - 14}{3 \cdot 5}$

Cancel the common factor.

$x \geq \frac{3 \cdot - 14}{3 \cdot 5}$

Rewrite the expression.

$x \geq \frac{- 14}{5}$

Move the negative in front of the fraction.

$x \geq - \frac{14}{5}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$x \geq - \frac{14}{5}$

Interval Notation:

$[- \frac{14}{5}, \infty)$

Solve the Inequality for x 5/2x<=6+5(2x+3)

Related Questions

Support LCMGCF.com by disabling your adblocker.