Absolute Value Question

Question

Find all numbers that are twice as far away from -3 as from 2. Create and solve an absolute value equation to show that you have found them all.

Answer 1

two numbers, 1/3 and 7

are twice as far from -3 as from 2

(2--3) = 5

5/3 = 1 2/3

2 x 1 2/3 = 3 1/3

3 1/3 is twice 1 2/3

-3+3 1/3 = 1/3

2- 1 2/3 = 1/3

1/3, between -3 and 2, is one number that is twice as far from -3

as it is from 2

3 1/3 is twice 1 2/3, 10/3 is twice 5/3

to the right of 2 is another number, 7, that is 5 from 2

and 10 from -3, 10 is twice 5

two numbers, 1/3 and 7, are twice as far from -3 as from 2

|-3+x| =2|2+x|

x=-1/3

|-3-1/3|= 3 1/3 from -3 to 1/3

2|2-1/3|= 4-2/3 = 3 1/3

2-1/3 = 1 1/3 from 1/3 to 2

x also = 7

|-3+7| = 10 from -3 to 7

|7-2| =5 from 2 to 7

1/3 and 7 are the only two numbers that are each twice as far from -3 as from 2

Answer 2

| -3 - x | = 2| 2 - x |

Assume both arguments are positive

-3 - x = 4 - 2x

x = 7

Assume both argumnets are negative

-(-3 - x) = (2)(-(2 - x)

3 + x = -4 - 2x

3x = -7

x = -7 / 3