Inequalities & Absolute Value

[walexthorpe]

Hi

I'm stuck on these two problem solutions found on pg 358 of the "Foundations of GMAT Math 5th Edition"

The first question reads: d + 3/2 < 8
in the answer though, I notice that 8 becomes 16/2 which is 8. But why was this done? Is it only to find a common ground for 3/2?

The second question reads: 4x/7 < 15 + x
How does 15 become 105? I'm not sure. I'm wondering if this is an error.

Could you please explain the answers?

Kind regards
Wayne

[RonPurewal]

Hi

I'm stuck on these two problem solutions found on pg 358 of the "Foundations of GMAT Math 5th Edition"

The first question reads: d + 3/2 < 8
in the answer though, I notice that 8 becomes 16/2 which is 8. But why was this done? Is it only to find a common ground for 3/2?

ya. you can't add or subtract fractions until they have a common denominator.

The second question reads: 4x/7 < 15 + x
How does 15 become 105? I'm not sure. I'm wondering if this is an error.

one of two things should be going on here.

1/
they might be multiplying by 7 on both sides, producing 4x < 105 + 7x.

2/
they might be giving everyone a common denominator of 7.
i.e., 4x/7 < 105/7 + x/7.
(in this case, the next step is to turn the equation into 4x < 105 + 7x anyway.)