Solve for y 8/(7y-2)=3

$\frac{8}{7 y - 2} = 3$

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.

$7 y - 2, 1$

Remove parentheses.

$7 y - 2, 1$

The LCM of one and any expression is the expression.

$7 y - 2$

Step 2

Multiply each term in $\frac{8}{7 y - 2} = 3$ by $7 y - 2$ to eliminate the fractions.

Multiply each term in $\frac{8}{7 y - 2} = 3$ by $7 y - 2$ .

$\frac{8}{7 y - 2} (7 y - 2) = 3 (7 y - 2)$

Simplify the left side.

Cancel the common factor of $7 y - 2$ .

Cancel the common factor.

$\frac{8}{7 y - 2} (7 y - 2) = 3 (7 y - 2)$

Rewrite the expression.

$8 = 3 (7 y - 2)$

Simplify the right side.

Apply the distributive property.

$8 = 3 (7 y) + 3 \cdot - 2$

Multiply.

Multiply $7$ by $3$ .

$8 = 21 y + 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$8 = 21 y - 6$

Step 3

Solve the equation.

Rewrite the equation as $21 y - 6 = 8$ .

$21 y - 6 = 8$

Move all terms not containing $y$ to the right side of the equation.

Add $6$ to both sides of the equation.

$21 y = 8 + 6$

Add $8$ and $6$ .

$21 y = 14$

Divide each term in $21 y = 14$ by $21$ and simplify.

Divide each term in $21 y = 14$ by $21$ .

$\frac{21 y}{21} = \frac{14}{21}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 y}{21} = \frac{14}{21}$

Divide $y$ by $1$ .

$y = \frac{14}{21}$

Simplify the right side.

Cancel the common factor of $14$ and $21$ .

Factor $7$ out of $14$ .

$y = \frac{7 (2)}{21}$

Cancel the common factors.

Factor $7$ out of $21$ .

$y = \frac{7 \cdot 2}{7 \cdot 3}$

Cancel the common factor.

$y = \frac{7 \cdot 2}{7 \cdot 3}$

Rewrite the expression.

$y = \frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{2}{3}$

Decimal Form:

$y = 0.\overline{6}$

Solve for y 8/(7y-2)=3

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