What is the justification for each step in solving the inequality? 3x+1/2<−x+4 Select from the drop-down menus to correctly justify each step.

see below

Step-by-step explanation:

(3x+1)/2<−x+4

Multiply each side by 2 using the multiplication property of equality

3x+1 < -2x +8

Subtract 1 from each side using the subtraction property of equality

3x < -2x+7

Add 2x to each side using the addition property of equality

5x < 7

Divide each side by 5 using the division property of equality

x < 7/5

Multiplication property.

Subtraction property.

Addition property.

Division property.

If Brandi purchases x albums and y singles, then x albums cost $10x and y singles cost $y. She wants to spend no more than $25 total, then

Brandi wants to purchase at least 5 singles. This means that

Note that x and y are whole numbers.  

There are three possibility:

x = 0,  y = 25 (the total cost is 10·0 + 1·25 = 25 ≤ 25 and 25 singles is more than 5 singles);x = 1,  y = 15 (the total cost is 10·1 + 1·15 = 25 ≤ 25 and 15 singles is more than 5 singles);x = 2,  y = 5 (the total cost is 10·2 + 1·5 = 25 ≤ 25 and 5 singles is equal to minimal required number of singles).

1) 0 albums and 25 singles;

2) 1 album and 15 singles;

3) 2 albums and 5 singles.