Solve 2x-5x-6/4 1/3(x-5)=-5x

Question

Solve the equation

x = - \frac{5}{3}

Alternative Form

x = - 1. \dot{6}

Evaluate

2 x - 5 x - \frac{6}{4} \times \frac{1}{3} (x - 5) = - 5 x

Simplify

More Steps

Evaluate

2 x - 5 x - \frac{6}{4} \times \frac{1}{3} (x - 5)

Cancel out the common factor 2

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms

- \frac{1}{2} (x - 5)

Apply the distributive property

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

Multiply the numbers

- \frac{1}{2} x - (- \frac{5}{2})

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}{2} x + \frac{5}{2}

2 x - 5 x - \frac{1}{2} x + \frac{5}{2}

Subtract the terms

More Steps

Evaluate

2 x - 5 x - \frac{1}{2} x

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

(2 - 5 - \frac{1}{2}) x

Subtract the numbers

- \frac{7}{2} x

- \frac{7}{2} x + \frac{5}{2}

- \frac{7}{2} x + \frac{5}{2} = - 5 x

Move the variable to the left side

- \frac{7}{2} x + \frac{5}{2} + 5 x = 0

Add the terms

More Steps

Evaluate

- \frac{7}{2} x + 5 x

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

(- \frac{7}{2} + 5) x

Add the numbers

More Steps

Evaluate

- \frac{7}{2} + 5

Reduce fractions to a common denominator

- \frac{7}{2} + \frac{5 \times 2}{2}

Write all numerators above the common denominator

\frac{- 7 + 5 \times 2}{2}

Multiply the numbers

\frac{- 7 + 10}{2}

Add the numbers

\frac{3}{2}

\frac{3}{2} x

\frac{3}{2} x + \frac{5}{2} = 0

Move the constant to the right side

\frac{3}{2} x = 0 - \frac{5}{2}

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

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

Multiply by the reciprocal

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

Multiply

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

Solution

More Steps

Evaluate

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

Reduce the numbers

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

Multiply the numbers

- \frac{5}{3}

x = - \frac{5}{3}

Alternative Form

x = - 1. \dot{6}

Show Solution

Rewrite the equation

3 x = - 5

Evaluate

2 x - 5 x - \frac{6}{4} \times \frac{1}{3} (x - 5) = - 5 x

Evaluate

More Steps

Evaluate

2 x - 5 x - \frac{6}{4} \times \frac{1}{3} (x - 5)

Cancel out the common factor 2

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms

- \frac{1}{2} (x - 5)

Apply the distributive property

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

Multiply the numbers

- \frac{1}{2} x - (- \frac{5}{2})

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}{2} x + \frac{5}{2}

2 x - 5 x - \frac{1}{2} x + \frac{5}{2}

Subtract the terms

More Steps

Evaluate

2 x - 5 x - \frac{1}{2} x

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

(2 - 5 - \frac{1}{2}) x

Subtract the numbers

- \frac{7}{2} x

- \frac{7}{2} x + \frac{5}{2}

- \frac{7}{2} x + \frac{5}{2} = - 5 x

Multiply both sides of the equation by LCD

- 7 x + 5 = - 10 x

Move the variable to the left side

3 x + 5 = 0

Solution

3 x = - 5

Show Solution

Solve the equation

Rewrite the equation

Graph