I am in dire need of assistance. Can anyone tell me the forumula/solution to transforming inqualities into equivalent inequalities with y alone on one side? I really don't understand this.
We can work with specific examples much better than not. If you have specific inequaliaties that are troubling you , post them, or a sample of them.
Oh, okay. Well, I've seen this before:
2x + 3y > 0
You handle it like an alg problem.
subtract 2x from each side.
3y>-2x
divide by 3
y>-2/3 x
that is it. Only one thing you have to be worried about, if you multiply or divide by a negative number, the inequality changes: example
2x-3y>15
-3y>15-2x
and here we divide by -3, watch the inequality sign reverse...
y<-5+2/3 x
Of course, I'd be happy to help you with transforming inequalities with y alone on one side. The process of rearranging inequalities involves similar steps to solving equations, with a few additional considerations. Here's a step-by-step guide:
Step 1: Start with the given inequality.
Step 2: Simplify the inequality by performing any necessary operations (such as combining like terms or distributing).
Step 3: Get rid of any constants or terms not involving y on the same side as y. To accomplish this, you'll need to use inverse operations (opposite operations) to isolate y.
Step 4: If there is a coefficient (a number multiplied by y), divide both sides of the inequality by that coefficient to isolate y.
Step 5: Finally, write down the inequality with y alone on one side. Be careful to remember that when you multiply or divide by a negative number, the direction of the inequality sign must be flipped.
Let's take an example to illustrate this process:
Suppose we have the inequality: 3y + 7 > 4y - 2
Step 1: Start with the given inequality: 3y + 7 > 4y - 2
Step 2: Simplify the inequality: 3y - 4y > -2 - 7
Step 3: Combine like terms: -y > -9
Step 4: Divide both sides by -1 to isolate y, remembering to change the direction of the inequality sign: y < 9
Step 5: Write down the final inequality with y alone on one side: y < 9
So, the solution to the given inequality, with y alone on one side, is y < 9.
Remember to always perform the same operation (such as adding, subtracting, multiplying, or dividing) to both sides of the inequality to maintain its equivalence.