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QuestionSimplify the expression using order of operations: 2[5+4(7⋅4−24)]=2[5+4(7 \cdot 4-24)]=

Studdy Solution

STEP 1

Assumptions1. We are given the expression [5+4(7⋅4−24)][5+4(7 \cdot4-24)]. We need to simplify this expression using the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often abbreviated as PEMAS.

STEP 2

First, we need to perform the operation inside the innermost parentheses. This is the multiplication and subtraction operation in the expression (7⋅4−24)(7 \cdot4-24).
2[5+4(7⋅4−24)]=2[5+4(28−24)]2[5+4(7 \cdot4-24)] =2[5+4(28-24)]

STEP 3

Next, we perform the subtraction inside the parentheses.
2[5+(28−24)]=2[5+()]2[5+(28-24)] =2[5+()]

STEP 4

Now, we perform the multiplication operation inside the brackets, which is 4(4)4(4).
2[+4(4)]=2[+16]2[+4(4)] =2[+16]

STEP 5

Next, we perform the addition operation inside the brackets, which is 5+165+16.
2[5+16]=2[21]2[5+16] =2[21]

STEP 6

Finally, we perform the multiplication operation outside the brackets, which is 2[21]2[21].
2[21]=422[21] =42So, the simplified expression is 4242.

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