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 \( 24(34 + x) = 1,200 \), here is the reasoning behind the given step:

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

Reasoning:

1. Distributive Property: The step is derived by using the distributive property of multiplication over addition. Specifically, the left side of the equation \( 24(34 + x) \) is expanded into two parts: \[ 24 \times 34 + 24 \times x \] This means you multiply \( 24 \) by both \( 34 \) and \( x \).

2. Calculating \( 24 \times 34 \): \[ 24 \times 34 = 816 \] This is the calculation performed using multiplication.

3. Combining Results: The equation now transforms from \( 24(34 + x) = 1,200 \) to \( 816 + 24x = 1,200 \) after performing the multiplication.

Therefore, the transition from the original equation to Step 1 is done by applying the distributive property and simplifying \( 24(34) \) to \( 816 \).

Answer 2

To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.

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

Step 2: 816 − 816 + 24x = 1,200 − 816

Answer 3

To transition from Step 1 \( 816 + 24x = 1,200 \) to Step 2 \( 816 - 816 + 24x = 1,200 - 816 \), here’s the reasoning:

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

Reasoning:

1. Isolating the Variable: The intention in this step is to isolate \( 24x \) on one side of the equation. To do this, we need to eliminate the constant term \( 816 \) from the left side.

2. Subtraction of Equal Values: By subtracting \( 816 \) from both sides of the equation, we ensure that the equation remains balanced. According to the property of equality, whatever you do to one side of an equation, you must do to the other side. Therefore: \[ (816 + 24x) - 816 = (1,200) - 816 \]

3. Simplifying: The left side simplifies to \( 24x \) (since \( 816 - 816 = 0 \)): \[ 0 + 24x = 1,200 - 816 \] Hence, we can write it as: \[ 24x = 1,200 - 816 \]

In summary, in Step 2, the operation performed is the subtraction of \( 816 \) from both sides of the equation to isolate \( 24x \), which maintains the equality of the equation.

Answer 4

To solve the equation: 24(34+x)=1,200
, give the reasons for each of the given steps.

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

Step 3: 24x=384

Answer 5

To transition from Step 2 \( 816 - 816 + 24x = 1,200 - 816 \) (which simplifies to \( 24x = 1,200 - 816 \)) to Step 3 \( 24x = 384 \), here’s the reasoning:

Step 3: \( 24x = 384 \)

Reasoning:

1. Performing the Subtraction: In Step 2, we established the equation \( 24x = 1,200 - 816 \). The next step involves calculating the right side, which requires performing the subtraction: \[ 1,200 - 816 \] When you calculate this, you find: \[ 1,200 - 816 = 384 \]

2. Substituting the Value: After computing the right side, you can replace \( 1,200 - 816 \) with \( 384 \) in the equation. This leads to the equation: \[ 24x = 384 \]

In summary, in Step 3, the calculation of \( 1,200 - 816 \) is performed, yielding \( 384 \), which allows us to express the equation simply as \( 24x = 384 \).