Solve -4x- 2/3 (3x-9)-5> 2x

Question

Solve the inequality

x < \frac{1}{8}

Alternative Form

x \in (- \infty, \frac{1}{8})

Evaluate

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

Simplify

More Steps

Evaluate

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

Multiply the terms

More Steps

Evaluate

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

Apply the distributive property

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

Multiply the numbers

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

Multiply the numbers

- 2 x - (- 6)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 2 x + 6

- 4 x - 2 x + 6 - 5

Subtract the terms

More Steps

Evaluate

- 4 x - 2 x

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

(- 4 - 2) x

Subtract the numbers

- 6 x

- 6 x + 6 - 5

Subtract the numbers

- 6 x + 1

- 6 x + 1 > 2 x

Move the variable to the left side

- 6 x + 1 - 2 x > 0

Subtract the terms

More Steps

Evaluate

- 6 x - 2 x

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

(- 6 - 2) x

Subtract the numbers

- 8 x

- 8 x + 1 > 0

Move the constant to the right side

- 8 x > 0 - 1

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

- 8 x > - 1

Change the signs on both sides of the inequality and flip the inequality sign

8 x < 1

Divide both sides

\frac{8 x}{8} < \frac{1}{8}

Solution

x < \frac{1}{8}

Alternative Form

x \in (- \infty, \frac{1}{8})

Show Solution