Solve for x (5x-2)/(3x)=7

$\frac{5 x - 2}{3 x} = 7$

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 x, 1$

The LCM of one and any expression is the expression.

$3 x$

Step 2

Multiply each term in $\frac{5 x - 2}{3 x} = 7$ by $3 x$ to eliminate the fractions.

Multiply each term in $\frac{5 x - 2}{3 x} = 7$ by $3 x$ .

$\frac{5 x - 2}{3 x} (3 x) = 7 (3 x)$

Simplify the left side.

Rewrite using the commutative property of multiplication.

$3 \frac{5 x - 2}{3 x} x = 7 (3 x)$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$3 \frac{5 x - 2}{3 (x)} x = 7 (3 x)$

Cancel the common factor.

$3 \frac{5 x - 2}{3 x} x = 7 (3 x)$

Rewrite the expression.

$\frac{5 x - 2}{x} x = 7 (3 x)$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{5 x - 2}{x} x = 7 (3 x)$

Rewrite the expression.

$5 x - 2 = 7 (3 x)$

Simplify the right side.

Multiply $3$ by $7$ .

$5 x - 2 = 21 x$

Step 3

Solve the equation.

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

Subtract $21 x$ from both sides of the equation.

$5 x - 2 - 21 x = 0$

Subtract $21 x$ from $5 x$ .

$- 16 x - 2 = 0$

Add $2$ to both sides of the equation.

$- 16 x = 2$

Divide each term in $- 16 x = 2$ by $- 16$ and simplify.

Divide each term in $- 16 x = 2$ by $- 16$ .

$\frac{- 16 x}{- 16} = \frac{2}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 x}{- 16} = \frac{2}{- 16}$

Divide $x$ by $1$ .

$x = \frac{2}{- 16}$

Simplify the right side.

Cancel the common factor of $2$ and $- 16$ .

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{- 16}$

Cancel the common factors.

Factor $2$ out of $- 16$ .

$x = \frac{2 \cdot 1}{2 \cdot - 8}$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot - 8}$

Rewrite the expression.

$x = \frac{1}{- 8}$

Move the negative in front of the fraction.

$x = - \frac{1}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{8}$

Decimal Form:

$x = - 0.125$

Solve for x (5x-2)/(3x)=7

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