Solve the Inequality for x 3/5(x-12)>x-24

$\frac{3}{5} (x - 12) > x - 24$

Step 1

Simplify $\frac{3}{5} \cdot (x - 12)$ .

Rewrite.

$0 + 0 + \frac{3}{5} \cdot (x - 12) > x - 24$

Simplify by adding zeros.

$\frac{3}{5} \cdot (x - 12) > x - 24$

Apply the distributive property.

$\frac{3}{5} x + \frac{3}{5} \cdot - 12 > x - 24$

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

$\frac{3 x}{5} + \frac{3}{5} \cdot - 12 > x - 24$

Multiply $\frac{3}{5} \cdot - 12$ .

Combine $\frac{3}{5}$ and $- 12$ .

$\frac{3 x}{5} + \frac{3 \cdot - 12}{5} > x - 24$

Multiply $3$ by $- 12$ .

$\frac{3 x}{5} + \frac{- 36}{5} > x - 24$

Move the negative in front of the fraction.

$\frac{3 x}{5} - \frac{36}{5} > x - 24$

Step 2

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

Subtract $x$ from both sides of the inequality.

$\frac{3 x}{5} - \frac{36}{5} - x > - 24$

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

$\frac{3 x}{5} - x \cdot \frac{5}{5} - \frac{36}{5} > - 24$

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

$\frac{3 x}{5} + \frac{- x \cdot 5}{5} - \frac{36}{5} > - 24$

Combine the numerators over the common denominator.

$\frac{3 x - x \cdot 5}{5} - \frac{36}{5} > - 24$

Combine the numerators over the common denominator.

$\frac{3 x - x \cdot 5 - 36}{5} > - 24$

Multiply $5$ by $- 1$ .

$\frac{3 x - 5 x - 36}{5} > - 24$

Subtract $5 x$ from $3 x$ .

$\frac{- 2 x - 36}{5} > - 24$

Factor $2$ out of $- 2 x - 36$ .

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

$\frac{2 (- x) - 36}{5} > - 24$

Factor $2$ out of $- 36$ .

$\frac{2 (- x) + 2 (- 18)}{5} > - 24$

Factor $2$ out of $2 (- x) + 2 (- 18)$ .

$\frac{2 (- x - 18)}{5} > - 24$

Factor $- 1$ out of $- x$ .

$\frac{2 (- (x) - 18)}{5} > - 24$

Rewrite $- 18$ as $- 1 (18)$ .

$\frac{2 (- (x) - 1 (18))}{5} > - 24$

Factor $- 1$ out of $- (x) - 1 (18)$ .

$\frac{2 (- (x + 18))}{5} > - 24$

Rewrite $- (x + 18)$ as $- 1 (x + 18)$ .

$\frac{2 (- 1 (x + 18))}{5} > - 24$

Move the negative in front of the fraction.

$- \frac{2 (x + 18)}{5} > - 24$

Step 3

Divide each term in $- \frac{2 (x + 18)}{5} > - 24$ by $- 1$ and simplify.

Divide each term in $- \frac{2 (x + 18)}{5} > - 24$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{2 (x + 18)}{5}}{- 1} < \frac{- 24}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{2 (x + 18)}{5}}{1} < \frac{- 24}{- 1}$

Divide $\frac{2 (x + 18)}{5}$ by $1$ .

$\frac{2 (x + 18)}{5} < \frac{- 24}{- 1}$

Simplify the right side.

Divide $- 24$ by $- 1$ .

$\frac{2 (x + 18)}{5} < 24$

Step 4

Multiply both sides by $5$ .

$\frac{2 (x + 18)}{5} \cdot 5 < 24 \cdot 5$

Step 5

Simplify.

Simplify the left side.

Simplify $\frac{2 (x + 18)}{5} \cdot 5$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{2 (x + 18)}{5} \cdot 5 < 24 \cdot 5$

Rewrite the expression.

$2 (x + 18) < 24 \cdot 5$

Apply the distributive property.

$2 x + 2 \cdot 18 < 24 \cdot 5$

Multiply $2$ by $18$ .

$2 x + 36 < 24 \cdot 5$

Simplify the right side.

Multiply $24$ by $5$ .

$2 x + 36 < 120$

Step 6

Solve for $x$ .

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

Subtract $36$ from both sides of the inequality.

$2 x < 120 - 36$

Subtract $36$ from $120$ .

$2 x < 84$

Divide each term in $2 x < 84$ by $2$ and simplify.

Divide each term in $2 x < 84$ by $2$ .

$\frac{2 x}{2} < \frac{84}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{84}{2}$

Divide $x$ by $1$ .

$x < \frac{84}{2}$

Simplify the right side.

Divide $84$ by $2$ .

$x < 42$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x < 42$

Interval Notation:

$(- \infty, 42)$

Solve the Inequality for x 3/5(x-12)>x-24

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