Solve 1/8r-1/3r 9/8-7

Question

Simplify the expression

- \frac{1}{4} r - 7

Evaluate

\frac{1}{8} r - \frac{1}{3} r \times \frac{9}{8} - 7

Multiply the terms

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Multiply the terms

- \frac{1}{3} r \times \frac{9}{8}

Multiply the terms

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Evaluate

\frac{1}{3} \times \frac{9}{8}

Reduce the numbers

1 \times \frac{3}{8}

Multiply the numbers

\frac{3}{8}

- \frac{3}{8} r

\frac{1}{8} r - \frac{3}{8} r - 7

Solution

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Evaluate

\frac{1}{8} r - \frac{3}{8} r

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

(\frac{1}{8} - \frac{3}{8}) r

Subtract the numbers

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Evaluate

\frac{1}{8} - \frac{3}{8}

Write all numerators above the common denominator

\frac{1 - 3}{8}

Subtract the numbers

\frac{- 2}{8}

Cancel out the common factor 2

\frac{- 1}{4}

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

- \frac{1}{4}

- \frac{1}{4} r

- \frac{1}{4} r - 7

Show Solution

Factor the expression

- \frac{1}{4} (r + 28)

Evaluate

\frac{1}{8} r - \frac{1}{3} r \times \frac{9}{8} - 7

Multiply the terms

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Multiply the terms

\frac{1}{3} r \times \frac{9}{8}

Multiply the terms

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Evaluate

\frac{1}{3} \times \frac{9}{8}

Reduce the numbers

1 \times \frac{3}{8}

Multiply the numbers

\frac{3}{8}

\frac{3}{8} r

\frac{1}{8} r - \frac{3}{8} r - 7

Subtract the terms

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Simplify

\frac{1}{8} r - \frac{3}{8} r

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

(\frac{1}{8} - \frac{3}{8}) r

Subtract the numbers

More Steps

Evaluate

\frac{1}{8} - \frac{3}{8}

Write all numerators above the common denominator

\frac{1 - 3}{8}

Subtract the numbers

\frac{- 2}{8}

Cancel out the common factor 2

\frac{- 1}{4}

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

- \frac{1}{4}

- \frac{1}{4} r

- \frac{1}{4} r - 7

Solution

- \frac{1}{4} (r + 28)

Show Solution

Find the roots

r = - 28

Evaluate

\frac{1}{8} r - \frac{1}{3} r \times \frac{9}{8} - 7

To find the roots of the expression,set the expression equal to 0

\frac{1}{8} r - \frac{1}{3} r \times \frac{9}{8} - 7 = 0

Multiply the terms

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Multiply the terms

\frac{1}{3} r \times \frac{9}{8}

Multiply the terms

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Evaluate

\frac{1}{3} \times \frac{9}{8}

Reduce the numbers

1 \times \frac{3}{8}

Multiply the numbers

\frac{3}{8}

\frac{3}{8} r

\frac{1}{8} r - \frac{3}{8} r - 7 = 0

Subtract the terms

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Simplify

\frac{1}{8} r - \frac{3}{8} r

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

(\frac{1}{8} - \frac{3}{8}) r

Subtract the numbers

More Steps

Evaluate

\frac{1}{8} - \frac{3}{8}

Write all numerators above the common denominator

\frac{1 - 3}{8}

Subtract the numbers

\frac{- 2}{8}

Cancel out the common factor 2

\frac{- 1}{4}

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

- \frac{1}{4}

- \frac{1}{4} r

- \frac{1}{4} r - 7 = 0

Move the constant to the right-hand side and change its sign

- \frac{1}{4} r = 0 + 7

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

- \frac{1}{4} r = 7

Change the signs on both sides of the equation

\frac{1}{4} r = - 7

Multiply by the reciprocal

\frac{1}{4} r \times 4 = - 7 \times 4

Multiply

r = - 7 \times 4

Solution

r = - 28

Show Solution