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Math  /  Numbers & Operations

Question14. Find the value of each expression.  a. ∣−2⋅2∣+13−17−2.2=−4∣ −∣1 b. ∣5+(−3)∣−11=93+∈−3=2∣2∣=22−11=−9\begin{array}{l} \text { a. }|-2 \cdot 2|+13-17-2.2=-4 \\ \left\lvert\, \begin{array}{l} -\mid 1 \\ \text { b. }|5+(-3)|-11=9 \\ 3+\in-3=2|2|=2 \quad 2-11=-9 \end{array}\right. \end{array}

Studdy Solution

STEP 1

1. Each expression needs to be evaluated step by step.
2. Absolute values are to be calculated first.
3. Follow the order of operations: parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right).

STEP 2

1. Evaluate expression (a).
2. Evaluate expression (b).

STEP 3

Evaluate the absolute value and multiplication in expression (a).
∣−2⋅2∣=∣−4∣=4|-2 \cdot 2| = |-4| = 4

STEP 4

Substitute the evaluated absolute value back into the expression and simplify.
4+13−17−2.24 + 13 - 17 - 2.2

STEP 5

Perform the addition and subtraction from left to right.
4+13=174 + 13 = 17 17−17=017 - 17 = 0 0−2.2=−2.20 - 2.2 = -2.2

STEP 6

Evaluate the absolute value in expression (b).
∣5+(−3)∣=∣2∣=2|5 + (-3)| = |2| = 2

STEP 7

Substitute the evaluated absolute value back into the expression and simplify.
2−112 - 11

STEP 8

Perform the subtraction.
2−11=−92 - 11 = -9
The evaluated expressions are: a. −2.2-2.2 b. −9-9

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