Solve 20 (3/5 y-2- 3/2 y)=22y

Question

Solve the equation

y = - 1

Evaluate

20 (\frac{3}{5} y - 2 - \frac{3}{2} y) = 22 y

Subtract the terms

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Evaluate

\frac{3}{5} y - \frac{3}{2} y

Collect like terms by calculating the sum or difference of their coefficients

(\frac{3}{5} - \frac{3}{2}) y

Subtract the numbers

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Evaluate

\frac{3}{5} - \frac{3}{2}

Reduce fractions to a common denominator

\frac{3 \times 2}{5 \times 2} - \frac{3 \times 5}{2 \times 5}

Multiply the numbers

\frac{3 \times 2}{10} - \frac{3 \times 5}{2 \times 5}

Multiply the numbers

\frac{3 \times 2}{10} - \frac{3 \times 5}{10}

Write all numerators above the common denominator

\frac{3 \times 2 - 3 \times 5}{10}

Multiply the numbers

\frac{6 - 3 \times 5}{10}

Multiply the numbers

\frac{6 - 15}{10}

Subtract the numbers

\frac{- 9}{10}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{9}{10}

- \frac{9}{10} y

20 (- \frac{9}{10} y - 2) = 22 y

Expand the expression

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Evaluate

20 (- \frac{9}{10} y - 2)

Apply the distributive property

20 (- \frac{9}{10} y) - 20 \times 2

Multiply the numbers

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Evaluate

20 (- \frac{9}{10})

Multiplying or dividing an odd number of negative terms equals a negative

- 20 \times \frac{9}{10}

Reduce the numbers

- 2 \times 9

Multiply the numbers

- 18

- 18 y - 20 \times 2

Multiply the numbers

- 18 y - 40

- 18 y - 40 = 22 y

Move the variable to the left side

- 18 y - 40 - 22 y = 0

Subtract the terms

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Evaluate

- 18 y - 22 y

Collect like terms by calculating the sum or difference of their coefficients

(- 18 - 22) y

Subtract the numbers

- 40 y

- 40 y - 40 = 0

Move the constant to the right side

- 40 y = 0 + 40

Removing 0 doesn't change the value,so remove it from the expression

- 40 y = 40

Change the signs on both sides of the equation

40 y = - 40

Divide both sides

\frac{40 y}{40} = \frac{- 40}{40}

Divide the numbers

y = \frac{- 40}{40}

Solution

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Evaluate

\frac{- 40}{40}

Reduce the numbers

\frac{- 1}{1}

Calculate

- 1

y = - 1

Show Solution

Rewrite the equation

Rewrite in standard form

Rewrite in slope-intercept form

y = - 1

Evaluate

20 (\frac{3}{5} y - 2 - \frac{3}{2} y) = 22 y

Evaluate

More Steps

Evaluate

20 (\frac{3}{5} y - 2 - \frac{3}{2} y)

Subtract the terms

More Steps

Evaluate

\frac{3}{5} y - \frac{3}{2} y

Collect like terms by calculating the sum or difference of their coefficients

(\frac{3}{5} - \frac{3}{2}) y

Subtract the numbers

- \frac{9}{10} y

20 (- \frac{9}{10} y - 2)

20 (- \frac{9}{10} y - 2) = 22 y

Multiply

More Steps

Evaluate

20 (- \frac{9}{10} y - 2)

Apply the distributive property

20 (- \frac{9}{10} y) - 20 \times 2

Multiply the numbers

More Steps

Evaluate

20 (- \frac{9}{10})

Multiplying or dividing an odd number of negative terms equals a negative

- 20 \times \frac{9}{10}

Reduce the numbers

- 2 \times 9

Multiply the numbers

- 18

- 18 y - 20 \times 2

Multiply the numbers

- 18 y - 40

- 18 y - 40 = 22 y

Move the variable to the left side

- 40 y - 40 = 0

Move the constant to the right side

- 40 y = 40

Multiply both sides

40 y = - 40

Solution

y = - 1

Show Solution

Solve the equation

Rewrite the equation

Graph