Posted by **Anonymous** on Thursday, October 21, 2010 at 9:53pm.

one number is three more than a second number. Three times the first is 7 less than 2 times the second. Find the numbers.

The value of the second number is ___

- math -
**Reiny**, Thursday, October 21, 2010 at 10:05pm
second number ---- x

first number ------ x+3

A lot of students have difficulty translating an English inequality statement like "Three times the first is 7 less than 2 times the second" into an equation.

Here is the way I used to teach this: ..

Re-word the statement as

"Three times the first is less than 2 times the second by 7"

now translate that

3(x+3) < 2(x) by 7

let's add that difference of 7 to the smaller side, now they would be equal

3(x+3) + 7 = 2(x)

3x + 9 + 7 = 2x

x = -16

so second number is -16, he first is -13

check:

3 times the first = 3(-13) = -39

2 times the second = 2(-16) = -32

is -39 7 less than -32 ??? YEAHH!

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