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Problem 4

# Evaluate $$2-\\{5+(2-3)+[2-(3-4)]\\}$$

Expert verified
The evaluated expression is $$-5$$, found by following the order of operations (PEMDAS/BODMAS) and simplifying the innermost parentheses first, then working outward.
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## Unlock all solutions

In the given expression, identify the innermost parentheses (or brackets) and perform the operation inside those first. Here, the innermost parentheses are $$(2-3)$$ and $$(3-4)$$. First, let's simplify these two parenthetical expressions: $$2 - 3 = -1$$ $$3 - 4 = -1$$ Now, substitute these values back into the original expression: $$2 - \{5 + (-1) + [2 - (-1)]\}$$.

## Step 2: Simplify the expression inside the other parentheses

Next, perform the operations inside the other parentheses (or brackets) - in this case, the square brackets [ ]. Continuing with the simplification, we now have: $$2 - \{5 + (-1) + [2 - (-1)]\} = 2 - \{5 + (-1) + [2 + 1]\}$$ Now, add 2 and 1 inside the square brackets: $$2 - \{5 + (-1) + 3\}$$

## Step 3: Simplify the entire expression inside the curly brackets

Now, perform the operations inside the curly brackets { }. Add and subtract in the order they appear: $$2 - \{5 + (-1) + 3\} = 2 - \{4 + 3\}$$ Now, add 4 and 3 inside the curly brackets: $$2 - \{7\}$$

## Step 4: Subtract the value in the curly brackets from 2

Finally, subtract the value inside the curly brackets from 2: $$2 - 7 = -5$$ So, the evaluated expression is: $$-5$$

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