Solve for y 1/5(45y-5)=6y-20

$\frac{1}{5} (45 y - 5) = 6 y - 20$

Step 1

Simplify $\frac{1}{5} \cdot (45 y - 5)$ .

Rewrite.

$0 + 0 + \frac{1}{5} \cdot (45 y - 5) = 6 y - 20$

Simplify by adding zeros.

$\frac{1}{5} \cdot (45 y - 5) = 6 y - 20$

Apply the distributive property.

$\frac{1}{5} (45 y) + \frac{1}{5} \cdot - 5 = 6 y - 20$

Cancel the common factor of $5$ .

Factor $5$ out of $45 y$ .

$\frac{1}{5} (5 (9 y)) + \frac{1}{5} \cdot - 5 = 6 y - 20$

Cancel the common factor.

$\frac{1}{5} (5 (9 y)) + \frac{1}{5} \cdot - 5 = 6 y - 20$

Rewrite the expression.

$9 y + \frac{1}{5} \cdot - 5 = 6 y - 20$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$9 y + \frac{1}{5} \cdot (5 (- 1)) = 6 y - 20$

Cancel the common factor.

$9 y + \frac{1}{5} \cdot (5 \cdot - 1) = 6 y - 20$

Rewrite the expression.

$9 y - 1 = 6 y - 20$

Step 2

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

Subtract $6 y$ from both sides of the equation.

$9 y - 1 - 6 y = - 20$

Subtract $6 y$ from $9 y$ .

$3 y - 1 = - 20$

Step 3

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

Add $1$ to both sides of the equation.

$3 y = - 20 + 1$

Add $- 20$ and $1$ .

$3 y = - 19$

Step 4

Divide each term in $3 y = - 19$ by $3$ and simplify.

Divide each term in $3 y = - 19$ by $3$ .

$\frac{3 y}{3} = \frac{- 19}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 19}{3}$

Divide $y$ by $1$ .

$y = \frac{- 19}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{19}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{19}{3}$

Decimal Form:

$y = - 6.\overline{3}$

Mixed Number Form:

$y = - 6 \frac{1}{3}$

Solve for y 1/5(45y-5)=6y-20

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