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Math  /  Numbers & Operations

Question1. Simplify the following expressions: a) −8+∣5−7∣-8+|5-7| b) 2⋅∣4−9∣−32 \cdot|4-9|-3 c) ∣6−2∣2−5\frac{|6-2|}{2}-5

Studdy Solution

STEP 1

1. We are simplifying mathematical expressions involving absolute values.
2. The absolute value of a number is its distance from zero on the number line, which is always non-negative.
3. We will perform arithmetic operations following the order of operations (PEMDAS/BODMAS).

STEP 2

1. Simplify expression a) −8+∣5−7∣-8 + |5 - 7|.
2. Simplify expression b) 2⋅∣4−9∣−32 \cdot |4 - 9| - 3.
3. Simplify expression c) ∣6−2∣2−5\frac{|6 - 2|}{2} - 5.

STEP 3

Calculate the absolute value in the expression −8+∣5−7∣ -8 + |5 - 7| .
∣5−7∣=∣−2∣=2 |5 - 7| = |-2| = 2

STEP 4

Substitute the absolute value back into the expression and simplify.
−8+2=−6 -8 + 2 = -6

STEP 5

Calculate the absolute value in the expression 2⋅∣4−9∣−3 2 \cdot |4 - 9| - 3 .
∣4−9∣=∣−5∣=5 |4 - 9| = |-5| = 5

STEP 6

Substitute the absolute value back into the expression and simplify.
2⋅5−3=10−3=7 2 \cdot 5 - 3 = 10 - 3 = 7

STEP 7

Calculate the absolute value in the expression ∣6−2∣2−5\frac{|6 - 2|}{2} - 5.
∣6−2∣=∣4∣=4 |6 - 2| = |4| = 4

STEP 8

Substitute the absolute value back into the expression and simplify.
42−5=2−5=−3 \frac{4}{2} - 5 = 2 - 5 = -3
The simplified expressions are: a) −6-6 b) 77 c) −3-3

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