Examkin

Soru

Zorluk: OrtaAbsolute Value

If x=−3x = -3, what is the value of the expression 8−3∣2x−7∣8 - 3|2x - 7|?

  1. -31Cevap
  2. B
    5
  3. C
    47
  4. D
    65

Cevap

-31
The expression is evaluated using the correct order of operations. First, the value inside the absolute value is simplified by substituting -3, yielding -13. The absolute value of -13 is positive 13. Finally, multiplying 13 by 3 gives 39, and subtracting 39 from 8 results in -31.

Adım Adım Çözüm

1
Substitute -3 for x in the expression.
8−3∣2(−3)−7∣8 - 3|2(-3) - 7|
To evaluate the expression for the specific variable value.
2
Multiply the numbers inside the absolute value.
8−3∣−6−7∣8 - 3|-6 - 7|
Following the order of operations, calculations grouped inside absolute value bars must be simplified first.
3
Subtract the remaining numbers inside the absolute value.
8−3∣−13∣8 - 3|-13|
Continuing to simplify the contents within the absolute value grouping.
4
Evaluate the absolute value of -13.
8−3(13)8 - 3(13)
The absolute value of any non-zero number is its positive distance from zero.
5
Multiply 3 by 13.
8−398 - 39
According to the order of operations (PEMDAS), multiplication must be performed before subtraction.
6
Subtract 39 from 8.
-31
This is the final operation to find the total value of the expression.

Anahtar Kavram

Evaluating absolute value expressions with order of operations
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Konular

Absolute Value

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