Missing Step 1: Solving The Math Expression

Hey guys! Let's break down this math problem step-by-step to figure out the missing expression. We're given a mathematical expression and a few steps of its solution, but one step is missing. Our mission is to find that missing piece of the puzzle. So, buckle up, and let's dive in!

Understanding the Problem

We're given the expression $[(-10+2)-1]+(2+3)$ and told that the solution process involves three steps. We know Step 2 is $-9+2+3$ and Step 3 is $-7+3$. The challenge is to figure out what Step 1 should be. This means we need to understand the order of operations and how the expression is simplified at each stage.

To figure out the missing Step 1, let's backtrack from Step 2. Remember the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This tells us the order in which we should perform the operations.

Breaking Down the Steps

To pinpoint the missing Step 1, we need to carefully examine the original expression and how it transforms into Step 2. The original expression is $[(-10+2)-1]+(2+3)$. Let's think about what operations we can perform first according to PEMDAS.

The innermost parentheses are $(-10+2)$. This is the first thing we should simplify. So, the key is to correctly perform this operation. Then we will compare the result with the options provided.

Now, let’s dive deeper into the expression and analyze it piece by piece. The given expression is $[(-10 + 2) - 1] + (2 + 3)$. The first part we need to tackle is the innermost parentheses: $(-10 + 2)$. This is a simple addition of two numbers with different signs.

Let’s perform the calculation:

• -10 + 2 = -8

So, the innermost parentheses simplify to -8. Now we can substitute this back into the original expression. This gives us a clearer picture of how the expression evolves from one step to the next. By focusing on each part of the expression, we can methodically simplify it and reveal the missing step.

Analyzing the Options

Now, let's look at the options provided and see which one matches our deduction for Step 1. This involves comparing each option to what we expect Step 1 to be based on our simplification of the original expression.

We have the following options:

A. $[8+1]+(2+3)$ B. $[-8-1]+(2+3)$ C. $[-10+1]+(2+3)$ D. $[-10+-1+2]+(2+3)$

Our goal is to find the option that correctly represents the first step in simplifying the original expression, which is $[(-10+2)-1]+(2+3)$. We've already identified that the first operation to perform is within the innermost parentheses: $(-10 + 2)$. Let's see which option reflects this initial simplification.

We know that $-10 + 2 = -8$. So, the expression inside the square brackets should become $(-8 - 1)$. The other part of the expression, $(2 + 3)$, remains unchanged at this stage because we haven't performed any operations on it yet. Therefore, we are looking for an option that has $(-8 - 1)$ inside the square brackets and $(2 + 3)$ as the second part of the expression. By carefully comparing each option, we can identify the one that accurately reflects this intermediate step.

Identifying the Correct Step 1

Now, let’s pinpoint the correct Step 1 by comparing our simplified expression with the given options. We've determined that the first step involves simplifying $(-10 + 2)$ to $-8$, so the expression should look like $[-8 - 1] + (2 + 3)$.

Looking at the options:

A. $[8+1]+(2+3)$ - This is incorrect because the signs and numbers don't match our simplification. B. $[-8-1]+(2+3)$ - This looks promising! It matches our expected form. C. $[-10+1]+(2+3)$ - This is incorrect because it doesn't reflect the simplification of $(-10 + 2)$. D. $[-10+-1+2]+(2+3)$ - This is incorrect as it seems to have rearranged terms without proper simplification.

Option B, $[-8-1]+(2+3)$, perfectly matches our expected Step 1. It correctly substitutes $(-10 + 2)$ with $-8$ and maintains the rest of the expression. The second part, $(2+3)$, remains untouched as it should.

So, the missing Step 1 is indeed $[-8-1]+(2+3)$. This step accurately reflects the first simplification in the original expression, setting the stage for the subsequent steps.

Verifying the Next Steps

To be absolutely sure, let's verify that this Step 1 logically leads to the given Step 2 and Step 3. This will give us confidence that we've correctly identified the missing step and understand the flow of the solution.

If Step 1 is $[-8-1]+(2+3)$, let's see how it leads to Step 2, which is $-9+2+3$. In Step 1, we have two sets of parentheses. Let's simplify them individually.

• First set: $-8 - 1 = -9$
• Second set: $2 + 3 = 5$

Substituting these results back into Step 1, we get $-9 + 5$. However, Step 2 is given as $-9 + 2 + 3$. We need to examine how $5$ in Step 1 transforms into $2 + 3$ in Step 2. This seems correct because they are just rewriting $5$ as $2+3$.

Now, let’s see how Step 2, $-9 + 2 + 3$, leads to Step 3, which is $-7 + 3$. We can perform the addition from left to right:

• $-9 + 2 = -7$

So, the expression becomes $-7 + 3$, which exactly matches Step 3. This confirms that our identified Step 1 logically flows into the given subsequent steps. By verifying this progression, we can be confident in our solution and understanding of the problem.

Final Answer

So, guys, after carefully analyzing the expression and the given steps, we've successfully identified the missing Step 1. The correct expression for Step 1 is:

B. $[-8-1]+(2+3)$

This step accurately reflects the initial simplification of the original expression, setting the stage for the subsequent steps in the solution. Great job working through this problem with me! Math can be fun when we break it down piece by piece, right? Keep practicing, and you'll become a pro at solving these kinds of problems in no time! Remember, the key is to understand the order of operations and to work methodically through each step. You got this!