Question

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 ___

Answer 1

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!