Question

Justify each step of the solution by stating the property that was used to get to each step.
Given: 4.5(8-x)+36=102-2.5(3x+24)
Step 1: 36-4.5x+36=102-7.5x-60
Step 2: 72-4.5x=42-7.5x
Step 3: 72+3x=42
Step 4: 3x=-30
Step 5: x=-10

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