Solve x/3-2 1/2=4x/9-2x/3

Question

Solve the equation

x = \frac{9}{2}

Alternative Form

x = 4.5

Evaluate

\frac{x}{3} - 2 \frac{1}{2} = (4 \times \frac{x}{9}) - (2 \times \frac{x}{3})

Covert the mixed number to an improper fraction

More Steps

Evaluate

2 \frac{1}{2}

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

\frac{2 \times 2 + 1}{2}

Multiply the terms

\frac{4 + 1}{2}

Add the terms

\frac{5}{2}

\frac{x}{3} - \frac{5}{2} = (4 \times \frac{x}{9}) - (2 \times \frac{x}{3})

Simplify

More Steps

Evaluate

(4 \times \frac{x}{9}) - (2 \times \frac{x}{3})

Multiply the terms

\frac{4 x}{9} - (2 \times \frac{x}{3})

Multiply the terms

\frac{4 x}{9} - \frac{2 x}{3}

\frac{x}{3} - \frac{5}{2} = \frac{4 x}{9} - \frac{2 x}{3}

Multiply both sides of the equation by LCD

(\frac{x}{3} - \frac{5}{2}) \times 18 = (\frac{4 x}{9} - \frac{2 x}{3}) \times 18

Simplify the equation

More Steps

Evaluate

(\frac{x}{3} - \frac{5}{2}) \times 18

Apply the distributive property

\frac{x}{3} \times 18 - \frac{5}{2} \times 18

Simplify

x \times 6 - 5 \times 9

Use the commutative property to reorder the terms

6 x - 5 \times 9

Multiply the numbers

6 x - 45

6 x - 45 = (\frac{4 x}{9} - \frac{2 x}{3}) \times 18

Simplify the equation

More Steps

Evaluate

(\frac{4 x}{9} - \frac{2 x}{3}) \times 18

Apply the distributive property

\frac{4 x}{9} \times 18 - \frac{2 x}{3} \times 18

Simplify

4 x \times 2 - 2 x \times 6

Multiply the numbers

8 x - 2 x \times 6

Multiply the numbers

8 x - 12 x

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

(8 - 12) x

Subtract the numbers

- 4 x

6 x - 45 = - 4 x

Move the variable to the left side

6 x - 45 + 4 x = 0

Add the terms

More Steps

Evaluate

6 x + 4 x

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

(6 + 4) x

Add the numbers

10 x

10 x - 45 = 0

Move the constant to the right side

10 x = 0 + 45

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

10 x = 45

Divide both sides

\frac{10 x}{10} = \frac{45}{10}

Divide the numbers

x = \frac{45}{10}

Solution

x = \frac{9}{2}

Alternative Form

x = 4.5

Show Solution

Rewrite the equation

2 x = 9

Evaluate

\frac{x}{3} - 2 \frac{1}{2} = (4 \times \frac{x}{9}) - (2 \times \frac{x}{3})

Covert the mixed number to an improper fraction

More Steps

Evaluate

\frac{x}{3} - 2 \frac{1}{2}

Covert the mixed number to an improper fraction

More Steps

Evaluate

2 \frac{1}{2}

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

\frac{2 \times 2 + 1}{2}

Multiply the terms

\frac{4 + 1}{2}

Add the terms

\frac{5}{2}

\frac{x}{3} - \frac{5}{2}

\frac{x}{3} - \frac{5}{2} = (4 \times \frac{x}{9}) - (2 \times \frac{x}{3})

Evaluate

More Steps

Evaluate

(4 \times \frac{x}{9}) - (2 \times \frac{x}{3})

Multiply the terms

\frac{4 x}{9} - (2 \times \frac{x}{3})

Multiply the terms

\frac{4 x}{9} - \frac{2 x}{3}

\frac{x}{3} - \frac{5}{2} = \frac{4 x}{9} - \frac{2 x}{3}

Rewrite the expression

\frac{1}{3} x - \frac{5}{2} = \frac{4 x}{9} - \frac{2 x}{3}

Rewrite the expression

More Steps

Evaluate

\frac{4 x}{9} - \frac{2 x}{3}

Reduce the fraction

\frac{4}{9} x - \frac{2 x}{3}

Reduce the fraction

More Steps

Evaluate

- \frac{2 x}{3}

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

\frac{- 2 x}{3}

Reduce the fraction

- \frac{2}{3} x

\frac{4}{9} x - \frac{2}{3} x

\frac{1}{3} x - \frac{5}{2} = \frac{4}{9} x - \frac{2}{3} x

Multiply both sides of the equation by LCD

6 x - 45 = - 4 x

Move the variable to the left side

10 x - 45 = 0

Move the constant to the right side

10 x = 45

Solution

2 x = 9

Show Solution

Solve the equation

Rewrite the equation

Graph