Solve -1 > -2(x - 4) - 5(4x - 7)

Question

Solve the inequality

x > 2

Alternative Form

x \in (2, + \infty)

Evaluate

- 1 > - 2 (x - 4) - 5 (4 x - 7)

Swap the sides of the inequality

- 2 (x - 4) - 5 (4 x - 7) < - 1

Move the expression to the left side

- 2 (x - 4) - 5 (4 x - 7) - (- 1) < 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

- 2 (x - 4) - 5 (4 x - 7) + 1 < 0

Calculate the sum or difference

More Steps

Evaluate

- 2 (x - 4) - 5 (4 x - 7) + 1

Expand the expression

More Steps

Calculate

- 2 (x - 4)

Apply the distributive property

- 2 x - (- 2 \times 4)

Multiply the numbers

- 2 x - (- 8)

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 + 8

- 2 x + 8 - 5 (4 x - 7) + 1

Expand the expression

More Steps

Calculate

- 5 (4 x - 7)

Apply the distributive property

- 5 \times 4 x - (- 5 \times 7)

Multiply the numbers

- 20 x - (- 5 \times 7)

Multiply the numbers

- 20 x - (- 35)

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

- 20 x + 35

- 2 x + 8 - 20 x + 35 + 1

Subtract the terms

More Steps

Evaluate

- 2 x - 20 x

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

(- 2 - 20) x

Subtract the numbers

- 22 x

- 22 x + 8 + 35 + 1

Add the numbers

- 22 x + 44

- 22 x + 44 < 0

Move the constant to the right side

- 22 x < 0 - 44

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

- 22 x < - 44

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

22 x > 44

Divide both sides

\frac{22 x}{22} > \frac{44}{22}

Divide the numbers

x > \frac{44}{22}

Solution

More Steps

Evaluate

\frac{44}{22}

Reduce the numbers

\frac{2}{1}

Calculate

2

x > 2

Alternative Form

x \in (2, + \infty)

Show Solution