Which of the following is not a solution of ...

Question

Which of the following is not a solution of 10 > |4-2x|+6

a. 0

b. 1

c. 3.14

d. 3.99

Answer 1

The four choices are values of x. Just plug each x-value into the inequality to see if it's true. If it is, it's a solution. If it's not true, it isn't a solution. I'll do the first one (a) for you:

10 > |4-2x|+6

Plug in x = 0:

10 > |4 - 2·0| + 6

10 >| 4| + 6

10 > 10

10 is equal to 10 but it is NOT greater than itself. So choice a), x = 0, is not a solution. You try the other three.

Answer 2

Which of the following is not a solution of ...

Which of the following is not a solution of 10 > |4-2x|+6

a. 0

b. 1

c. 3.14

d. 3.99

The "solution" is the value of x that makes the inequality true.

One method of finding the value of x that DOES NOT MAKE THE INEQUALITY TRUE is to plug in the values given as choices and then see whether the inequality is true or false.

Another method (learned in Algebra class) is to "solve" for x as an inequality:

10 > |4-2x|+6

4 > |4-2x| (subtract +6 from both sides of inequality retains sense of inequality)

2 > |2-x| (divide all terms by +2 retains the sense of the inequality)

Either:

2 > +(2-x)

0 > -x (subtract 2 from both sides)

x > 0

Or:

2 > -(2-x)

4 > x

x < 4

For values of x as 0, 1, 3.14, and 3.99, the inequality IS TRUE IN EACH CASE. Since the problem asks "which are not a solution" and they are all solutions the answers are a, b, c, d.