Solve 2(7/2r-152r-3/27r-4)

Question

Simplify the expression

Solution

- \frac{2675}{9} r - 8

Evaluate

2 (\frac{7}{2} r - 152 r - \frac{3}{27} r - 4)

Cancel out the common factor 3

2 (\frac{7}{2} r - 152 r - \frac{1}{9} r - 4)

Subtract the terms

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Evaluate

\frac{7}{2} r - 152 r - \frac{1}{9} r - 4

Subtract the terms

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Evaluate

\frac{7}{2} r - 152 r - \frac{1}{9} r

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

(\frac{7}{2} - 152 - \frac{1}{9}) r

Subtract the numbers

- \frac{2675}{18} r

- \frac{2675}{18} r - 4

2 (- \frac{2675}{18} r - 4)

Apply the distributive property

2 (- \frac{2675}{18} r) - 2 \times 4

Multiply the numbers

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Evaluate

2 (- \frac{2675}{18})

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

- 2 \times \frac{2675}{18}

Reduce the numbers

- 1 \times \frac{2675}{9}

Multiply the numbers

- \frac{2675}{9}

- \frac{2675}{9} r - 2 \times 4

Solution

- \frac{2675}{9} r - 8

Show Solution

Factor the expression

Factor

- \frac{1}{9} (2675 r + 72)

Evaluate

2 (\frac{7}{2} r - 152 r - \frac{3}{27} r - 4)

Cancel out the common factor 3

2 (\frac{7}{2} r - 152 r - \frac{1}{9} r - 4)

Subtract the terms

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Simplify

\frac{7}{2} r - 152 r

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

(\frac{7}{2} - 152) r

Subtract the numbers

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Evaluate

\frac{7}{2} - 152

Reduce fractions to a common denominator

\frac{7}{2} - \frac{152 \times 2}{2}

Write all numerators above the common denominator

\frac{7 - 152 \times 2}{2}

Multiply the numbers

\frac{7 - 304}{2}

Subtract the numbers

\frac{- 297}{2}

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

- \frac{297}{2}

- \frac{297}{2} r

2 (- \frac{297}{2} r - \frac{1}{9} r - 4)

Subtract the terms

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Simplify

- \frac{297}{2} r - \frac{1}{9} r

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

(- \frac{297}{2} - \frac{1}{9}) r

Subtract the numbers

More Steps

Evaluate

- \frac{297}{2} - \frac{1}{9}

Reduce fractions to a common denominator

- \frac{297 \times 9}{2 \times 9} - \frac{2}{9 \times 2}

Multiply the numbers

- \frac{297 \times 9}{18} - \frac{2}{9 \times 2}

Multiply the numbers

- \frac{297 \times 9}{18} - \frac{2}{18}

Write all numerators above the common denominator

\frac{- 297 \times 9 - 2}{18}

Multiply the numbers

\frac{- 2673 - 2}{18}

Subtract the numbers

\frac{- 2675}{18}

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

- \frac{2675}{18}

- \frac{2675}{18} r

2 (- \frac{2675}{18} r - 4)

Factor the expression

2 (- \frac{1}{18}) (2675 r + 72)

Solution

- \frac{1}{9} (2675 r + 72)

Show Solution

Find the roots

Find the roots of the algebra expression

r = - \frac{72}{2675}

Alternative Form

r \approx - 0.026916

Evaluate

2 (\frac{7}{2} r - 152 r - \frac{3}{27} r - 4)

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

2 (\frac{7}{2} r - 152 r - \frac{3}{27} r - 4) = 0

Cancel out the common factor 3

2 (\frac{7}{2} r - 152 r - \frac{1}{9} r - 4) = 0

Subtract the terms

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Simplify

\frac{7}{2} r - 152 r

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

(\frac{7}{2} - 152) r

Subtract the numbers

More Steps

Evaluate

\frac{7}{2} - 152

Reduce fractions to a common denominator

\frac{7}{2} - \frac{152 \times 2}{2}

Write all numerators above the common denominator

\frac{7 - 152 \times 2}{2}

Multiply the numbers

\frac{7 - 304}{2}

Subtract the numbers

\frac{- 297}{2}

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

- \frac{297}{2}

- \frac{297}{2} r

2 (- \frac{297}{2} r - \frac{1}{9} r - 4) = 0

Subtract the terms

More Steps

Simplify

- \frac{297}{2} r - \frac{1}{9} r

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

(- \frac{297}{2} - \frac{1}{9}) r

Subtract the numbers

More Steps

Evaluate

- \frac{297}{2} - \frac{1}{9}

Reduce fractions to a common denominator

- \frac{297 \times 9}{2 \times 9} - \frac{2}{9 \times 2}

Multiply the numbers

- \frac{297 \times 9}{18} - \frac{2}{9 \times 2}

Multiply the numbers

- \frac{297 \times 9}{18} - \frac{2}{18}

Write all numerators above the common denominator

\frac{- 297 \times 9 - 2}{18}

Multiply the numbers

\frac{- 2673 - 2}{18}

Subtract the numbers

\frac{- 2675}{18}

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

- \frac{2675}{18}

- \frac{2675}{18} r

2 (- \frac{2675}{18} r - 4) = 0

Rewrite the expression

- \frac{2675}{18} r - 4 = 0

Move the constant to the right side

- \frac{2675}{18} r = 0 + 4

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

- \frac{2675}{18} r = 4

Change the signs on both sides of the equation

\frac{2675}{18} r = - 4

Multiply by the reciprocal

\frac{2675}{18} r \times \frac{18}{2675} = - 4 \times \frac{18}{2675}

Multiply

r = - 4 \times \frac{18}{2675}

Solution

More Steps

Evaluate

- 4 \times \frac{18}{2675}

Multiply the numbers

- \frac{4 \times 18}{2675}

Multiply the numbers

- \frac{72}{2675}

r = - \frac{72}{2675}

Alternative Form

r \approx - 0.026916

Show Solution

2(7/2r 152r 3/27r 4)

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression