If x satisfies the linear equation 4(x - 2) - 15 = 2x + 3 which of the following statement… — GRE General Test

x

satisfies the linear equation

4(x - 2) - 15 = 2x + 3

which of the following statements must be true? Select all that apply.

$x$ is a prime numberAnswer
$2x - 5$ is equal to $21$ Answer
$x + 7$ is a multiple of $5$ Answer
D
$x$ is an even integer
E
$\frac{x + 1}{2} = 6$

Answer

The correct statements are that

x

is a prime number,

2x - 5

is equal to

21

, and

x + 7

is a multiple of

5

Solving the equation

4(x - 2) - 15 = 2x + 3

yields

x = 13

. Evaluating the choices with

x = 13

confirms that

13

is a prime number,

2(13) - 5 = 21

, and

13 + 7 = 20

(a multiple of

5

Step-by-Step Solution

Expand the left side of the linear equation by distributing the constant term.

4x - 8 - 15 = 2x + 3

Distribution removes parentheses so like terms can be combined.

Combine constant terms on the left side of the equation.

4x - 23 = 2x + 3

Simplifying

-8 - 15

yields

-23

Isolate variable terms on the left side and constant terms on the right side by subtracting

2x

and adding

23

to both sides.

2x = 26

Subtracting

2x

gives

2x

on the left, and adding

23

gives

26

on the right.

Divide both sides of the equation by

2

to solve for

x

x = 13

Dividing

26

2

determines the unique value of

x

Test each statement using

x = 13

13

is prime (True);

2(13) - 5 = 21

(True);

13 + 7 = 20

which is a multiple of

5

(True);

13

is even (False);

\frac{13 + 1}{2} = 7 \neq 6

(False).

Direct evaluation identifies which statements hold true.

Key Concept

Solving linear equations in one variable and evaluating numerical properties of the solution.

Estimated Time:1m 0s

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