Question

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

Answer 1

Answer:

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

Step-by-step 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.

Answer 2

Answer:

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)

$-7$                                          (Division property of order)

Step-by-step 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.

$-7$

Hence proved.