Question

How do I solve this problem ½ y + 2 ≥ 1/3 y - 4 ?

Answer 1

`y>=-36`

Explanation:

When trying to solve an algebraic inequality for a variable, we can apply the same rules we use to solve an equation; however, we must maintain our inequality throughout the problem.

Our goal is to completely isolate `y`. Begin by subtracting `1/3y` from both sides, which causes `1/3y` to cancel out on the right side:

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

`1/2y-1/3y+2>=-4`

Simplify the left side by combining like terms (all terms containing `y`) :

`1/2y-1/3y=3/6y-2/6y=1/6y`

`1/6y+2>=-4`

Subtract `2` from each side, causing `2` to cancel out on the left side:

`1/6y+cancel2-cancel2>=-4-2`

`1/6y>=-6`

Multiply both sides by `6`, causing `1/6` to cancel out on the left side:

`cancel6cancel(1/6)y>=-6(6)`

`y>=-36`

• If we were multiplying or dividing either side by a negative number, the sign would switch (I.E., become `<=`); however, this does not happen here. The prospect of this happening is why we must maintain our inequality all throughout the problem.