Solve 5x-3(5x-8)<-7

Question

Solve the inequality

x > \frac{31}{10}

Alternative Form

x \in (\frac{31}{10}, + \infty)

Evaluate

5 x - 3 (5 x - 8) < - 7

Move the expression to the left side

5 x - 3 (5 x - 8) - (- 7) < 0

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 - 3 (5 x - 8) + 7 < 0

Calculate the sum or difference

More Steps

Evaluate

5 x - 3 (5 x - 8) + 7

Expand the expression

More Steps

Calculate

- 3 (5 x - 8)

Apply the distributive property

- 3 \times 5 x - (- 3 \times 8)

Multiply the numbers

- 15 x - (- 3 \times 8)

Multiply the numbers

- 15 x - (- 24)

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

- 15 x + 24

5 x - 15 x + 24 + 7

Subtract the terms

More Steps

Evaluate

5 x - 15 x

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

(5 - 15) x

Subtract the numbers

- 10 x

- 10 x + 24 + 7

Add the numbers

- 10 x + 31

- 10 x + 31 < 0

Move the constant to the right side

- 10 x < 0 - 31

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

- 10 x < - 31

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

10 x > 31

Divide both sides

\frac{10 x}{10} > \frac{31}{10}

Solution

x > \frac{31}{10}

Alternative Form

x \in (\frac{31}{10}, + \infty)

Show Solution