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- ___
what are these steps?

Answer 1

Sure! Let’s go through each of the steps provided in the equation \( 24(34+x) = 1,200 \) and the reasoning behind each transformation.

Original Equation:

\[ 24(34+x) = 1,200 \]

Step 1:

\( 816 + 24x = 1,200 \)

Reason: Here, you distributed the \( 24 \) across the terms in the parentheses. The calculation is as follows:

\[ 24 \cdot 34 + 24 \cdot x = 816 + 24x \]

So, \( 24(34) = 816 \).

Step 2:

\( 816 - 816 + 24x = 1,200 - 816 \)

Reason: You are isolating the \( 24x \) term by subtracting \( 816 \) from both sides of the equation. This is applying the property of equality which states that you can subtract the same number from both sides without changing the equality.

\[ 816 - 816 + 24x = 1,200 - 816 \]

Step 3:

\( 24x = 384 \)

Reason: This step results from simplifying both sides of the equation after performing the subtraction:

\[ 0 + 24x = 384 \]

Thus, it results in \( 24x = 384 \).

Step 4:

\( x = 16 \)

Reason: You divide both sides by \( 24 \) to isolate \( x \):

\[ \frac{24x}{24} = \frac{384}{24} \]

This simplifies to \( x = 16 \).

Summary of the Steps:

1. Distributed \( 24 \) to the parentheses.
2. Subtracted \( 816 \) from both sides to isolate the \( 24x \).
3. Simplified the equations by understanding that subtracting \( 816 \) from \( 1,200 \) equals \( 384 \).
4. Divided by \( 24 \) to solve for \( x \).

These steps clearly outline the logical progression to solve the equation \( 24(34+x) = 1,200 \).