Solve (5x-13/2)-(3x-17/3)=(13x-1/6)

Question

Solve the equation

x = - \frac{2}{33}

Alternative Form

x = - 0. \dot{0} \dot{6}

Evaluate

(5 x - \frac{13}{2}) - (3 x - \frac{17}{3}) = 13 x - \frac{1}{6}

Simplify

More Steps

Evaluate

(5 x - \frac{13}{2}) - (3 x - \frac{17}{3})

Remove the parentheses

5 x - \frac{13}{2} - (3 x - \frac{17}{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

5 x - \frac{13}{2} - 3 x + \frac{17}{3}

Subtract the terms

More Steps

Evaluate

5 x - 3 x

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

(5 - 3) x

Subtract the numbers

2 x

2 x - \frac{13}{2} + \frac{17}{3}

Add the numbers

More Steps

Evaluate

- \frac{13}{2} + \frac{17}{3}

Reduce fractions to a common denominator

- \frac{13 \times 3}{2 \times 3} + \frac{17 \times 2}{3 \times 2}

Multiply the numbers

- \frac{13 \times 3}{6} + \frac{17 \times 2}{3 \times 2}

Multiply the numbers

- \frac{13 \times 3}{6} + \frac{17 \times 2}{6}

Write all numerators above the common denominator

\frac{- 13 \times 3 + 17 \times 2}{6}

Multiply the numbers

\frac{- 39 + 17 \times 2}{6}

Multiply the numbers

\frac{- 39 + 34}{6}

Add the numbers

\frac{- 5}{6}

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

- \frac{5}{6}

2 x - \frac{5}{6}

2 x - \frac{5}{6} = 13 x - \frac{1}{6}

Multiply both sides of the equation by LCM

(2 x - \frac{5}{6}) \times 6 = (13 x - \frac{1}{6}) \times 6

Calculate

More Steps

Evaluate

(2 x - \frac{5}{6}) \times 6

Apply the distributive property

2 x \times 6 - \frac{5}{6} \times 6

Multiply the numbers

12 x - \frac{5}{6} \times 6

Multiply the numbers

More Steps

Evaluate

- \frac{5}{6} \times 6

Reduce the numbers

- 5 \times 1

Simplify

- 5

12 x - 5

12 x - 5 = (13 x - \frac{1}{6}) \times 6

Calculate

More Steps

Evaluate

(13 x - \frac{1}{6}) \times 6

Apply the distributive property

13 x \times 6 - \frac{1}{6} \times 6

Multiply the numbers

78 x - \frac{1}{6} \times 6

Multiply the numbers

More Steps

Evaluate

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

Reduce the numbers

- 1 \times 1

Simplify

- 1

78 x - 1

12 x - 5 = 78 x - 1

Move the expression to the left side

12 x - 5 - 78 x = - 1

Move the expression to the right side

12 x - 78 x = - 1 + 5

Add and subtract

More Steps

Evaluate

12 x - 78 x

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

(12 - 78) x

Subtract the numbers

- 66 x

- 66 x = - 1 + 5

Add and subtract

- 66 x = 4

Change the signs on both sides of the equation

66 x = - 4

Divide both sides

\frac{66 x}{66} = \frac{- 4}{66}

Divide the numbers

x = \frac{- 4}{66}

Solution

More Steps

Evaluate

\frac{- 4}{66}

Cancel out the common factor 2

\frac{- 2}{33}

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

- \frac{2}{33}

x = - \frac{2}{33}

Alternative Form

x = - 0. \dot{0} \dot{6}

Show Solution

Rewrite the equation

33 x = - 2

Evaluate

(5 x - \frac{13}{2}) - (3 x - \frac{17}{3}) = 13 x - \frac{1}{6}

Evaluate

More Steps

Evaluate

(5 x - \frac{13}{2}) - (3 x - \frac{17}{3})

Remove the parentheses

5 x - \frac{13}{2} - (3 x - \frac{17}{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

5 x - \frac{13}{2} - 3 x + \frac{17}{3}

Subtract the terms

More Steps

Evaluate

5 x - 3 x

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

(5 - 3) x

Subtract the numbers

2 x

2 x - \frac{13}{2} + \frac{17}{3}

Add the numbers

More Steps

Evaluate

- \frac{13}{2} + \frac{17}{3}

Reduce fractions to a common denominator

- \frac{13 \times 3}{2 \times 3} + \frac{17 \times 2}{3 \times 2}

Multiply the numbers

- \frac{13 \times 3}{6} + \frac{17 \times 2}{3 \times 2}

Multiply the numbers

- \frac{13 \times 3}{6} + \frac{17 \times 2}{6}

Write all numerators above the common denominator

\frac{- 13 \times 3 + 17 \times 2}{6}

Multiply the numbers

\frac{- 39 + 17 \times 2}{6}

Multiply the numbers

\frac{- 39 + 34}{6}

Add the numbers

\frac{- 5}{6}

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

- \frac{5}{6}

2 x - \frac{5}{6}

2 x - \frac{5}{6} = 13 x - \frac{1}{6}

Multiply both sides of the equation by LCD

12 x - 5 = 78 x - 1

Move the variable to the left side

- 66 x - 5 = - 1

Move the constant to the right side

- 66 x = 4

Multiply both sides

66 x = - 4

Solution

33 x = - 2

Show Solution

Solve the equation

Rewrite the equation

Graph