Question

Justify each step by identifying the property used. Like this one 1/2(y+3)>1/3(4-y)

Answer 1

`y>-(1)/(5)`

Explanation:

Given:

`(1)/(2)(y+3)>(1)/(3)(4-y)`

Step 1: Use distributive property:

`(1)/(2)y+3\cdot (1)/(2)>(1)/(3)\cdot 4-(1)/(3)y`

Step 2: Using addition property, add
`(1)/(3)y` to both sides of inequality:

`(1)/(2)y+(1)/(3)y+(3)/(2)>(4)/(3)-(1)/(3)y+(1)/(3)y\\ \\(1)/(2)y+(1)/(3)y+(3)/(2)>(4)/(3)`

Step 3: Using addition property, add
`-(3)/(2)` to both sides of inequality:

`(1)/(2)y+(1)/(3)y+(3)/(2)-(3)/(2)>(4)/(3)-(3)/(2)\\ \\(1)/(2)y+(1)/(3)y>(4)/(3)-(3)/(2)`

Step 4: Subtract fractions in the right side:

`(4)/(3)-(3)/(2)=(4\cdot 2-3\cdot 3)/(3\cdot 3)=-(1)/(6)`

Step 5: Use distributive property in left side:

`(1)/(2)y+(1)/(3)y=y\left((1)/(2)+(1)/(3)\right)=(3+2)/(2\cdot 3)y=(5)/(6)y`

You get the inequality:

`(5)/(6)y>-(1)/(6)`

Step 6: Use division property:

`y>-(1)/(6):(5)/(6)\\ \\y>-(1)/(6)\cdot (6)/(5)\\ \\y>-(1)/(5)`