Question

What is the reason for each step in the solution of the inequality?

4(x+6)>−5(x+5)−14

Select the reason for each step from the drop-down menus.

Answer 1

Statement Reason

`4(x+6)>-5(x+5)-14` (Given)

`4x+24>-5x-39` (Combine like terms)

`4x+63>-5x` (Addition property of order)

`63>-9x` (Subtraction property of order)

`-7<x` (Division property of order)

Explanation:

The given inequality is

`4(x+6)>-5(x+5)-14`

Using distributive property, we get

`4(x)+4(6)>-5(x)-5(5)-14`

`4x+24>-5x-25-14`

Combine like terms.

`4x+24>-5x-39`

Using addition property of order, add 39 on both sides.

`4x+24+39>-5x-39+39`

`4x+63>-5x`

Using subtraction property of order, subtract 4x from both sides.

`4x+63-4x>-5x-4x`

`63>-9x`

Using division property of order, divide both sides by -9. If we multiply or divide an inequality by a negative number, then the sign of inequality will change.

`-7<x`

Hence proved.

Answer 2

1. distributive property
2. combine like terms
3. division property of order

Explanation:

At the second step, parentheses have been eliminated. The distributive property is used for that.

At the third step, -25-14 is replaced by -39. This process is called combine like terms.

At the last step, the inequality is divided by the coefficient of x. The division is by a negative number, so the order symbol is reversed, according to the division property of order.