Question

which expression has the greatest value when x = -5?
a. 1 - x
b. -1 - x
c. \\(\frac{1}{x}\\)
d. \\(\frac{x}{-1}\\)

Explanation:

Step1: Substitute \( x = -5 \) into option a

Expression for a: \( 1 - x \)
Substitute \( x = -5 \): \( 1 - (-5) = 1 + 5 = 6 \)

Step2: Substitute \( x = -5 \) into option b

Expression for b: \( -1 - x \)
Substitute \( x = -5 \): \( -1 - (-5) = -1 + 5 = 4 \)

Step3: Substitute \( x = -5 \) into option c

Expression for c: \( \frac{1}{x} \)
Substitute \( x = -5 \): \( \frac{1}{-5} = -\frac{1}{5} = -0.2 \)

Step4: Substitute \( x = -5 \) into option d

Expression for d: \( \frac{x}{-1} \)
Substitute \( x = -5 \): \( \frac{-5}{-1} = 5 \)

Step5: Compare the values

Values obtained:

• Option a: \( 6 \)
• Option b: \( 4 \)
• Option c: \( -0.2 \)
• Option d: \( 5 \)

Among \( 6, 4, -0.2, 5 \), the greatest value is \( 6 \) which corresponds to option a.

Answer:

a. \( 1 - x \)