Solve 1/6(6/7x-12)-1/4(8/9-4/7x)

Question

Simplify the expression

\frac{2}{7} x - \frac{20}{9}

Evaluate

\frac{1}{6} (\frac{6}{7} x - 12) - \frac{1}{4} (\frac{8}{9} - \frac{4}{7} x)

Multiply the terms

More Steps

Evaluate

\frac{1}{6} (\frac{6}{7} x - 12)

Apply the distributive property

\frac{1}{6} \times \frac{6}{7} x - \frac{1}{6} \times 12

Multiply the numbers

More Steps

Evaluate

\frac{1}{6} \times \frac{6}{7}

Reduce the numbers

1 \times \frac{1}{7}

Multiply the numbers

\frac{1}{7}

\frac{1}{7} x - \frac{1}{6} \times 12

Multiply the numbers

More Steps

Evaluate

\frac{1}{6} \times 12

Reduce the numbers

1 \times 2

Simplify

2

\frac{1}{7} x - 2

\frac{1}{7} x - 2 - \frac{1}{4} (\frac{8}{9} - \frac{4}{7} x)

Multiply the terms

More Steps

Evaluate

\frac{1}{4} (\frac{8}{9} - \frac{4}{7} x)

Apply the distributive property

\frac{1}{4} \times \frac{8}{9} - \frac{1}{4} \times \frac{4}{7} x

Multiply the numbers

More Steps

Evaluate

\frac{1}{4} \times \frac{8}{9}

Reduce the numbers

1 \times \frac{2}{9}

Multiply the numbers

\frac{2}{9}

\frac{2}{9} - \frac{1}{4} \times \frac{4}{7} x

Multiply the numbers

More Steps

Evaluate

\frac{1}{4} \times \frac{4}{7}

Reduce the numbers

1 \times \frac{1}{7}

Multiply the numbers

\frac{1}{7}

\frac{2}{9} - \frac{1}{7} x

\frac{1}{7} x - 2 - (\frac{2}{9} - \frac{1}{7} 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{1}{7} x - 2 - \frac{2}{9} + \frac{1}{7} x

Add the terms

More Steps

Evaluate

\frac{1}{7} x + \frac{1}{7} x

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

(\frac{1}{7} + \frac{1}{7}) x

Add the numbers

More Steps

Evaluate

\frac{1}{7} + \frac{1}{7}

Write all numerators above the common denominator

\frac{1 + 1}{7}

Add the numbers

\frac{2}{7}

\frac{2}{7} x

\frac{2}{7} x - 2 - \frac{2}{9}

Solution

More Steps

Evaluate

- 2 - \frac{2}{9}

Reduce fractions to a common denominator

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

Write all numerators above the common denominator

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

Multiply the numbers

\frac{- 18 - 2}{9}

Subtract the numbers

\frac{- 20}{9}

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

- \frac{20}{9}

\frac{2}{7} x - \frac{20}{9}

Show Solution

Factor the expression

\frac{2}{63} (9 x - 70)

Evaluate

\frac{1}{6} (\frac{6}{7} x - 12) - \frac{1}{4} (\frac{8}{9} - \frac{4}{7} x)

Simplify

More Steps

Evaluate

\frac{1}{6} (\frac{6}{7} x - 12)

Apply the distributive property

\frac{1}{6} \times \frac{6}{7} x + \frac{1}{6} (- 12)

Multiply the terms

More Steps

Evaluate

\frac{1}{6} \times \frac{6}{7}

Reduce the numbers

1 \times \frac{1}{7}

Multiply the numbers

\frac{1}{7}

\frac{1}{7} x + \frac{1}{6} (- 12)

Multiply the terms

More Steps

Evaluate

\frac{1}{6} (- 12)

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

- \frac{1}{6} \times 12

Reduce the numbers

- 1 \times 2

Simplify

- 2

\frac{1}{7} x - 2

\frac{1}{7} x - 2 - \frac{1}{4} (\frac{8}{9} - \frac{4}{7} x)

Simplify

More Steps

Evaluate

- \frac{1}{4} (\frac{8}{9} - \frac{4}{7} x)

Apply the distributive property

- \frac{1}{4} \times \frac{8}{9} - \frac{1}{4} (- \frac{4}{7} x)

Multiply the terms

More Steps

Evaluate

- \frac{1}{4} \times \frac{8}{9}

Reduce the numbers

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

Multiply the numbers

- \frac{2}{9}

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

Multiply the terms

More Steps

Evaluate

- \frac{1}{4} (- \frac{4}{7})

Multiplying or dividing an even number of negative terms equals a positive

\frac{1}{4} \times \frac{4}{7}

Reduce the numbers

1 \times \frac{1}{7}

Multiply the numbers

\frac{1}{7}

- \frac{2}{9} + \frac{1}{7} x

\frac{1}{7} x - 2 - \frac{2}{9} + \frac{1}{7} x

Add the terms

More Steps

Evaluate

\frac{1}{7} x + \frac{1}{7} x

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

(\frac{1}{7} + \frac{1}{7}) x

Add the numbers

More Steps

Evaluate

\frac{1}{7} + \frac{1}{7}

Write all numerators above the common denominator

\frac{1 + 1}{7}

Add the numbers

\frac{2}{7}

\frac{2}{7} x

\frac{2}{7} x - 2 - \frac{2}{9}

Subtract the numbers

More Steps

Evaluate

- 2 - \frac{2}{9}

Reduce fractions to a common denominator

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

Write all numerators above the common denominator

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

Multiply the numbers

\frac{- 18 - 2}{9}

Subtract the numbers

\frac{- 20}{9}

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

- \frac{20}{9}

\frac{2}{7} x - \frac{20}{9}

Solution

\frac{2}{63} (9 x - 70)

Show Solution

Find the roots

x = \frac{70}{9}

Alternative Form

x = 7. \dot{7}

Evaluate

\frac{1}{6} (\frac{6}{7} x - 12) - \frac{1}{4} (\frac{8}{9} - \frac{4}{7} x)

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

\frac{1}{6} (\frac{6}{7} x - 12) - \frac{1}{4} (\frac{8}{9} - \frac{4}{7} x) = 0

Multiply the terms

More Steps

Evaluate

\frac{1}{6} (\frac{6}{7} x - 12)

Apply the distributive property

\frac{1}{6} \times \frac{6}{7} x - \frac{1}{6} \times 12

Multiply the numbers

More Steps

Evaluate

\frac{1}{6} \times \frac{6}{7}

Reduce the numbers

1 \times \frac{1}{7}

Multiply the numbers

\frac{1}{7}

\frac{1}{7} x - \frac{1}{6} \times 12

Multiply the numbers

More Steps

Evaluate

\frac{1}{6} \times 12

Reduce the numbers

1 \times 2

Simplify

2

\frac{1}{7} x - 2

\frac{1}{7} x - 2 - \frac{1}{4} (\frac{8}{9} - \frac{4}{7} x) = 0

Multiply the terms

More Steps

Evaluate

\frac{1}{4} (\frac{8}{9} - \frac{4}{7} x)

Apply the distributive property

\frac{1}{4} \times \frac{8}{9} - \frac{1}{4} \times \frac{4}{7} x

Multiply the numbers

More Steps

Evaluate

\frac{1}{4} \times \frac{8}{9}

Reduce the numbers

1 \times \frac{2}{9}

Multiply the numbers

\frac{2}{9}

\frac{2}{9} - \frac{1}{4} \times \frac{4}{7} x

Multiply the numbers

More Steps

Evaluate

\frac{1}{4} \times \frac{4}{7}

Reduce the numbers

1 \times \frac{1}{7}

Multiply the numbers

\frac{1}{7}

\frac{2}{9} - \frac{1}{7} x

\frac{1}{7} x - 2 - (\frac{2}{9} - \frac{1}{7} x) = 0

Subtract the terms

More Steps

Simplify

\frac{1}{7} x - 2 - (\frac{2}{9} - \frac{1}{7} 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{1}{7} x - 2 - \frac{2}{9} + \frac{1}{7} x

Add the terms

More Steps

Evaluate

\frac{1}{7} x + \frac{1}{7} x

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

(\frac{1}{7} + \frac{1}{7}) x

Add the numbers

\frac{2}{7} x

\frac{2}{7} x - 2 - \frac{2}{9}

Subtract the numbers

More Steps

Evaluate

- 2 - \frac{2}{9}

Reduce fractions to a common denominator

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

Write all numerators above the common denominator

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

Multiply the numbers

\frac{- 18 - 2}{9}

Subtract the numbers

\frac{- 20}{9}

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

- \frac{20}{9}

\frac{2}{7} x - \frac{20}{9}

\frac{2}{7} x - \frac{20}{9} = 0

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

\frac{2}{7} x = 0 + \frac{20}{9}

Add the terms

\frac{2}{7} x = \frac{20}{9}

Multiply by the reciprocal

\frac{2}{7} x \times \frac{7}{2} = \frac{20}{9} \times \frac{7}{2}

Multiply

x = \frac{20}{9} \times \frac{7}{2}

Solution

More Steps

Evaluate

\frac{20}{9} \times \frac{7}{2}

Reduce the numbers

\frac{10}{9} \times 7

Multiply the numbers

\frac{10 \times 7}{9}

Multiply the numbers

\frac{70}{9}

x = \frac{70}{9}

Alternative Form

x = 7. \dot{7}

Show Solution