Solved on Nov 01, 2023

Use the distributive property to solve $\frac{5 x}{3} - x = \frac{x}{15} - \frac{6}{5}$ .

STEP 1

Assumptions1. We are given the equation $\frac{5 x}{3}-x=\frac{x}{15}-\frac{6}{5}$ . . We need to solve for $x$ using the Distributive Property.

STEP 2

First, we need to simplify the equation. We can do this by finding a common denominator for the fractions on both sides of the equation. The common denominator for $$, $15$, and $5$ is $15$.

STEP 3

Multiply each term in the equation by $15$ to eliminate the fractions.
$15 \cdot \frac{5 x}{3} -15 \cdot x =15 \cdot \frac{x}{15} -15 \cdot \frac{6}{5}$

STEP 4

implify each term.
$25x -15x = x -18$

STEP 5

Combine like terms on both sides of the equation.
$10x = x -18$

STEP 6

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$10x - x = -18$

STEP 7

implify the left side of the equation.
$9x = -18$

STEP 8

Finally, divide both sides of the equation by $$ to solve for $x$.
$x = \frac{-18}{}$

STEP 9

implify the right side of the equation to find the value of $x$ .
$x = -2$ So, the solution to the equation is $x = -2$ .

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Use the distributive property to solve $\frac{5 x}{3} - x = \frac{x}{15} - \frac{6}{5}$ .

STEP 1

Assumptions1. We are given the equation $\frac{5 x}{3}-x=\frac{x}{15}-\frac{6}{5}$ . . We need to solve for $x$ using the Distributive Property.

STEP 2

First, we need to simplify the equation. We can do this by finding a common denominator for the fractions on both sides of the equation. The common denominator for $$, $15$, and $5$ is $15$.

STEP 3

Multiply each term in the equation by $15$ to eliminate the fractions.
$15 \cdot \frac{5 x}{3} -15 \cdot x =15 \cdot \frac{x}{15} -15 \cdot \frac{6}{5}$

STEP 4

implify each term.
$25x -15x = x -18$

STEP 5

Combine like terms on both sides of the equation.
$10x = x -18$

STEP 6

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$10x - x = -18$

STEP 7

implify the left side of the equation.
$9x = -18$

STEP 8

Finally, divide both sides of the equation by $$ to solve for $x$.
$x = \frac{-18}{}$

STEP 9

implify the right side of the equation to find the value of $x$ .
$x = -2$ So, the solution to the equation is $x = -2$ .

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Use the distributive property to solve 5x3−x=x15−65\frac{5 x}{3} - x = \frac{x}{15} - \frac{6}{5}35x​−x=15x​−56​.

STEP 1

Assumptions1. We are given the equation 5x3−x=x15−65\frac{5 x}{3}-x=\frac{x}{15}-\frac{6}{5}35x​−x=15x​−56​. . We need to solve for xxx using the Distributive Property.

STEP 2

First, we need to simplify the equation. We can do this by finding a common denominator for the fractions on both sides of the equation. The common denominator for $$, $15$, and $5$ is $15$.

STEP 3

Multiply each term in the equation by 151515 to eliminate the fractions.15⋅5x3−15⋅x=15⋅x15−15⋅6515 \cdot \frac{5 x}{3} -15 \cdot x =15 \cdot \frac{x}{15} -15 \cdot \frac{6}{5}15⋅35x​−15⋅x=15⋅15x​−15⋅56​

STEP 4

implify each term.25x−15x=x−1825x -15x = x -1825x−15x=x−18

STEP 5

Combine like terms on both sides of the equation.10x=x−1810x = x -1810x=x−18

STEP 6

Subtract xxx from both sides of the equation to isolate xxx on one side.10x−x=−1810x - x = -1810x−x=−18

STEP 7

implify the left side of the equation.9x=−189x = -189x=−18

STEP 8

Finally, divide both sides of the equation by $$ to solve for $x$.x=−18x = \frac{-18}{}x=−18​

STEP 9

implify the right side of the equation to find the value of xxx.x=−2x = -2x=−2So, the solution to the equation is x=−2x = -2x=−2.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Use the distributive property to solve $\frac{5 x}{3} - x = \frac{x}{15} - \frac{6}{5}$ .

Assumptions1. We are given the equation $\frac{5 x}{3}-x=\frac{x}{15}-\frac{6}{5}$ . . We need to solve for $x$ using the Distributive Property.

Multiply each term in the equation by $15$ to eliminate the fractions.
$15 \cdot \frac{5 x}{3} -15 \cdot x =15 \cdot \frac{x}{15} -15 \cdot \frac{6}{5}$

implify each term.
$25x -15x = x -18$

Combine like terms on both sides of the equation.
$10x = x -18$

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$10x - x = -18$

implify the left side of the equation.
$9x = -18$

Finally, divide both sides of the equation by $$ to solve for $x$.
$x = \frac{-18}{}$

implify the right side of the equation to find the value of $x$ .
$x = -2$ So, the solution to the equation is $x = -2$ .