Solve - 5/3 a= 1/2 (2/3 a-2 4/3a)

Question

Solve the equation

a = 0

Evaluate

- \frac{5}{3} a = \frac{1}{2} (\frac{2}{3} a - 2 \frac{4}{3} \times a)

Simplify

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Evaluate

\frac{1}{2} (\frac{2}{3} a - 2 \frac{4}{3} \times a)

Covert the mixed number to an improper fraction

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Convert the expressions

2 \frac{4}{3}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{2 \times 3 + 4}{3}

Multiply the terms

\frac{6 + 4}{3}

Add the terms

\frac{10}{3}

\frac{1}{2} (\frac{2}{3} a - \frac{10}{3} a)

Subtract the terms

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Simplify

\frac{2}{3} a - \frac{10}{3} a

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

(\frac{2}{3} - \frac{10}{3}) a

Subtract the numbers

- \frac{8}{3} a

\frac{1}{2} (- \frac{8}{3} a)

Multiply the numbers

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Evaluate

\frac{1}{2} (- \frac{8}{3})

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

- \frac{1}{2} \times \frac{8}{3}

Reduce the numbers

- 1 \times \frac{4}{3}

Multiply the numbers

- \frac{4}{3}

- \frac{4}{3} a

- \frac{5}{3} a = - \frac{4}{3} a

Add or subtract both sides

- \frac{5}{3} a - (- \frac{4}{3} a) = 0

Subtract the terms

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Evaluate

- \frac{5}{3} a - (- \frac{4}{3} a)

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

(- \frac{5}{3} - (- \frac{4}{3})) a

Subtract the terms

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Evaluate

- \frac{5}{3} - (- \frac{4}{3})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- \frac{5}{3} + \frac{4}{3}

Write all numerators above the common denominator

\frac{- 5 + 4}{3}

Add the numbers

\frac{- 1}{3}

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

- \frac{1}{3}

- \frac{1}{3} a

- \frac{1}{3} a = 0

Change the signs on both sides of the equation

\frac{1}{3} a = 0

Solution

a = 0

Show Solution

Solve the equation

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