On the real number line, the point P corresponds to the real number x. If |x - 3| = 7, whi… — GRE General Test

On the real number line, the point $P$ corresponds to the real number $x$ . If $|x - 3| = 7$ , which of the following is a possible value of $x + 5$ ?

A
$-9$
B
$-4$
$1$ Answer
D
$9$
E
$12$

Answer

The correct answer is

1

Solving

|x - 3| = 7

produces two possible values for

x

x = 10

and

x = -4

. Substituting

x = -4

into

x + 5

yields

-4 + 5 = 1

, which is listed among the choices.

Step-by-Step Solution

Set up the two linear equations defined by the absolute value equation

|x - 3| = 7

The two cases are

x - 3 = 7

and

x - 3 = -7

By definition of absolute value,

|k| = 7

means

k = 7

k = -7

Solve each case for

x

From

x - 3 = 7

x = 10

. From

x - 3 = -7

x = -4

Adding

3

to both sides of each equation isolates

x

Evaluate

x + 5

for both solutions of

x

x = 10

x + 5 = 15

. If

x = -4

x + 5 = 1

Substitute each possible value of

x

into the expression

x + 5

Key Concept

Absolute Value as Distance on the Number Line

Estimated Time:45s

Question

Answer

Step-by-Step Solution

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