Question

What is the solution to the inequality below? 2(x -1) - 4(x + 2) < 5x

Answer 1

Answer:

$\boxed {x > -\frac{10}{7}}$

Step-by-step explanation:

Solve the given inequality:

$2(x - 1) - 4(x + 2) < 5x$

-Use Distributive Property:

$2(x - 1) - 4(x + 2) < 5x$

$2x - 2 - 4x - 8 < 5x$

-Combine like terms:

$2x - 2 - 4x - 8 < 5x$

$-2x - 10 < 5x$

-Subtract both sides by $5x$:

$-2x - 10 - 5x < 5x - 5x$

$-7x - 10 < 0$

-Add both sides by $10$:

$-7x - 10 + 10 < + 10$

$-7x < 10$

-When you are dividing a integer by a negative integer, the inequality sign would change. So, divide both sides by $-7$:

$\frac{-7x}{-7} < \frac{10}{-7}$

$\boxed {x > -\frac{10}{7}}$ (final answer)