To solve the equation: 24(34+x)=1,200

Question

, give the reasons for each of the given steps.

What was done to the previous step to get to the current equation?

Step 1: 816 + 24x = 1,200_______

Step 2: 816 − 816 + 24x = 1,200 − 816_______

Step 3: 24x = 384_______

Step 4: x = 16 _______

options:
1. Multiplication as the inverse operation to isolate the variable
2. Combine Like terms
3. Addition as the inverse operation to isolate the variable
4. Division as the inverse operation to isolate the variable

Answer 1

Let's analyze each step of the solution to the equation $24(34+x)=1,200$ and provide the reasoning for each step based on the options given.

Step 1: $816+24x=1,200$

This step involves expanding the left side of the equation:

• Reason: This is where you distribute the $24$ across the parentheses. $$24(34)+24(x)=816+24x$$

Step 2: $816-816+24x=1,200-816$

Here, $816$ is subtracted from both sides of the equation:

• Reason: This step is applying the property of equality, specifically using Addition as the inverse operation to isolate the variable $x$. By moving $816$ to the other side, the equation is simplified: $$24x=1,200-816$$

Step 3: $24x=384$

In this step, the right side of the equation is simplified:

• Reason: Combine Like Terms. The subtraction $1,200-816$ results in $384$, thereby simplifying the equation further.

Step 4: $x=16$

This step involves isolating $x$ by dividing both sides by $24$:

• Reason: This step uses Division as the inverse operation to isolate the variable $x$. Thus, $$x=\frac{384}{24}=16$$

Summary of Steps with corresponding reasons:

1. Step 1: Distribution (Expansion)
2. Step 2: Addition as the inverse operation to isolate the variable
3. Step 3: Combine Like Terms
4. Step 4: Division as the inverse operation to isolate the variable

The correct options for the reasons are:

• Step 2: 3. Addition as the inverse operation to isolate the variable
• Step 3: 2. Combine Like Terms
• Step 4: 4. Division as the inverse operation to isolate the variable