Solve 8(5x-4)-15x<5(15x)-19

Question

Solve the inequality

x > - \frac{13}{50}

Alternative Form

x \in (- \frac{13}{50}, + \infty)

Evaluate

8 (5 x - 4) - 15 x < 5 \times 15 x - 19

Multiply the numbers

8 (5 x - 4) - 15 x < 75 x - 19

Move the expression to the left side

8 (5 x - 4) - 15 x - (75 x - 19) < 0

Subtract the terms

More Steps

Evaluate

8 (5 x - 4) - 15 x - (75 x - 19)

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

8 (5 x - 4) - 15 x - 75 x + 19

Subtract the terms

More Steps

Evaluate

- 15 x - 75 x

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

(- 15 - 75) x

Subtract the numbers

- 90 x

8 (5 x - 4) - 90 x + 19

8 (5 x - 4) - 90 x + 19 < 0

Calculate the sum or difference

More Steps

Evaluate

8 (5 x - 4) - 90 x + 19

Expand the expression

More Steps

Calculate

8 (5 x - 4)

Apply the distributive property

8 \times 5 x - 8 \times 4

Multiply the numbers

40 x - 8 \times 4

Multiply the numbers

40 x - 32

40 x - 32 - 90 x + 19

Subtract the terms

More Steps

Evaluate

40 x - 90 x

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

(40 - 90) x

Subtract the numbers

- 50 x

- 50 x - 32 + 19

Add the numbers

- 50 x - 13

- 50 x - 13 < 0

Move the constant to the right side

- 50 x < 0 + 13

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

- 50 x < 13

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

50 x > - 13

Divide both sides

\frac{50 x}{50} > \frac{- 13}{50}

Divide the numbers

x > \frac{- 13}{50}

Solution

x > - \frac{13}{50}

Alternative Form

x \in (- \frac{13}{50}, + \infty)

Show Solution