Question

Justify each step of the solution by stating the property that was used to get to each step.

Answer 1

For this case we have the following expression:

$4.5 (8-x) + 36 = 102-2.5 (3x + 24)$

Applying distributive property to the terms within parentheses we have:

$36-4.5x + 36 = 102-7.5x-60$

We add similar terms on both sides of equality considering that:

Equal signs are added and the same sign is placed.

Different signs are subtracted and the major sign is placed.

$72-4.5x = 42-7.5x$

We add 7.5x to both sides of equality:

$72 + 3x = 42$

We subtract 72 from both sides of equality:

$3x = -30$

We divide between 3 on both sides of equality

$x = -10$

ANswer:

Distributive property

Add similar terms

Equality property of the sum

Equality subtraction property

Equality property of the division