Dwayne tried to evaluate an expression. Here is his work:

Question

3+542–(5–2)2
=
3+542–32 Step 1
=
3+5[16–9] Step 2
=
3+57 Step 3
=
3+35 Step 4
=
38 Step 5
Is Dwayne's work correct?

Answer 1

Let's carefully evaluate the expression $3+542-(5-2)2$ step by step to see if Dwayne's work is correct.

1. Original Expression: $$3+542-(5-2)2$$

2. Calculate the parentheses: $$5-2=3$$ So, now the expression becomes: $$3+542-3\cdot 2$$

3. Multiply: $$3\cdot 2=6$$ Now, the expression is: $$3+542-6$$

4. Calculate $542-6$: $$542-6=536$$ So now we have: $$3+536$$

5. Add: $$3+536=539$$

So the final result of the expression $3+542-(5-2)2$ is $539$.

Now, looking at Dwayne's work:

• In Step 1, he correctly simplifies $3+542-(5-2)2$ to $3+542-32$.
• However, in Step 2, he incorrectly simplifies $32$ as $32=16-9$, which is incorrect. $32=32$.
• The errors continue from there, and he ends up with a final answer of $38$, which is not correct.

Hence, Dwayne's work is not correct. The correct answer to the expression is $539$.