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

Answer 1

To solve the equation \( 24(34+x) = 1,200 \) and understand the steps taken, we can break down the process:

Given Step 1: \( 816 + 24x = 1,200 \)

Reason for this step:

The original equation \( 24(34+x)=1,200 \) involves distributing the \( 24 \) through the parentheses. This is done using the distributive property, which states that \( a(b+c) = ab + ac \).

Here, we apply the distributive property: \[ 24(34) + 24(x) = 1,200 \] Calculating \( 24 \times 34 \): \[ 24 \times 34 = 816 \] So the equation becomes: \[ 816 + 24x = 1,200 \]

In summary:

What was done to get from the original equation to Step 1?

• The \( 24 \) was distributed across \( (34 + x) \) using the distributive property, resulting in \( 816 + 24x = 1,200 \).

Answer 2

Step 2: 816 − 816 + 24x = 1,200 − 816

Answer 3

Given Step 2: \( 816 - 816 + 24x = 1,200 - 816 \)

Reason for this step:

In this step, we are isolating the term involving \( x \). This is done by subtracting \( 816 \) from both sides of the equation.

Breakdown:

1. Subtraction of 816 from both sides:

   • The equation from Step 1 is \( 816 + 24x = 1,200 \).
   • To isolate \( 24x \), we subtract \( 816 \) from both sides to maintain the equality of the equation.

2. Resulting equation:

   • On the left side: \( 816 - 816 + 24x = 0 + 24x \) simplifies to \( 24x \).
   • On the right side: \( 1,200 - 816 = 384 \).

Thus, we obtain: \[ 24x = 384 \]

In summary:

What was done to get from Step 1 to Step 2?

• \( 816 \) was subtracted from both sides of the equation to isolate \( 24x \), resulting in the equation \( 24x = 384 \).