Solve 2/5(1/3x-15/8)-1/3(1/2-2/3x)

Question

Simplify the expression

\frac{16}{45} x - \frac{11}{12}

Evaluate

\frac{2}{5} (\frac{1}{3} x - \frac{15}{8}) - \frac{1}{3} (\frac{1}{2} - \frac{2}{3} x)

Multiply the terms

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\frac{2}{15} x - \frac{3}{4} - \frac{1}{3} (\frac{1}{2} - \frac{2}{3} x)

Multiply the terms

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\frac{2}{15} x - \frac{3}{4} - (\frac{1}{6} - \frac{2}{9} x)

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{2}{15} x - \frac{3}{4} - \frac{1}{6} + \frac{2}{9} x

Add the terms

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\frac{16}{45} x - \frac{3}{4} - \frac{1}{6}

Solution

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\frac{16}{45} x - \frac{11}{12}

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Factor the expression

\frac{1}{180} (64 x - 165)

Evaluate

\frac{2}{5} (\frac{1}{3} x - \frac{15}{8}) - \frac{1}{3} (\frac{1}{2} - \frac{2}{3} x)

Simplify

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\frac{2}{15} x - \frac{3}{4} - \frac{1}{3} (\frac{1}{2} - \frac{2}{3} x)

Simplify

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\frac{2}{15} x - \frac{3}{4} - \frac{1}{6} + \frac{2}{9} x

Add the terms

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\frac{16}{45} x - \frac{3}{4} - \frac{1}{6}

Subtract the numbers

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\frac{16}{45} x - \frac{11}{12}

Solution

\frac{1}{180} (64 x - 165)

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Find the roots

x = \frac{165}{64}

Alternative Form

x = 2.578125

Evaluate

\frac{2}{5} (\frac{1}{3} x - \frac{15}{8}) - \frac{1}{3} (\frac{1}{2} - \frac{2}{3} x)

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

\frac{2}{5} (\frac{1}{3} x - \frac{15}{8}) - \frac{1}{3} (\frac{1}{2} - \frac{2}{3} x) = 0

Multiply the terms

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\frac{2}{15} x - \frac{3}{4} - \frac{1}{3} (\frac{1}{2} - \frac{2}{3} x) = 0

Multiply the terms

More Steps

\frac{2}{15} x - \frac{3}{4} - (\frac{1}{6} - \frac{2}{9} x) = 0

Subtract the terms

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\frac{16}{45} x - \frac{11}{12} = 0

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

\frac{16}{45} x = 0 + \frac{11}{12}

Add the terms

\frac{16}{45} x = \frac{11}{12}

Multiply by the reciprocal

\frac{16}{45} x \times \frac{45}{16} = \frac{11}{12} \times \frac{45}{16}

Multiply

x = \frac{11}{12} \times \frac{45}{16}

Solution

More Steps

x = \frac{165}{64}

Alternative Form

x = 2.578125

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