Algebra

[sienaaaa]

Hello, I'm having trouble with this one multiple choice problem:

Solve -2(y - 2) < 2(y - 4)

The possible solutions are:

A {y l y > 3}
B {y l y >1}
C {y l y > -3}
D {y l y < 3}

Can anyone help me?

 

[srmichael]

Hello, I'm having trouble with this one multiple choice problem:

Solve -2(y - 2) < 2(y - 4)

The possible solutions are:

A {y l y > 3}
B {y l y >1}
C {y l y > -3}
D {y l y < 3}

Can anyone help me?

What have you tried so far?

 

[sienaaaa]

What have you tried so far?

So far I distributed, and got
-2y+4 < 2y - 8

Then I canceled out both 2y's, and flipped the less than sign.

so I got 4> -8

Obviously this isn't the right answer though

 

[srmichael]

So far I distributed, and got
-2y+4 < 2y - 8 ---> Correct!

Then I canceled out both 2y's, and flipped the less than sign.

so I got 4> -8

Obviously this isn't the right answer though

The red above is your mistake. The 2y terms do not cancel out.

-2y + 4 < 2y - 8

Add 2y to both sides:

4 < 4y - 8

Add 8 to both sides:

12 < 4y

Divide both sides by 4:

3 < y or y > 3...Answer A

Make sense?

 

[sienaaaa]

wow, yeah. thank you. That makes much more sense.

 

[HallsofIvy]

By the way, rather than distributing the "2", you might have found it simpler to divide both sides by the (positive) number, 2, to get -(y- 2)< y- 4. Then distribute: -y+ 2< y- 4. Add y to both sides and add 4 to both sides: 6< 2y. Finally, divide both sides by the (positive) number, 2: 3< y.

(I emphasize that the numbers are positive because, of course, multiplying or dividing both sides of an inequality by a negative number changes the direction of the inequality. If we had divided both sides of -2(y- 2)< 2(y- 4) by -2, we would have gotten y- 2> -(y- 4) which would eventually give y> 3.