Question

1. Which equation has the same solution for x as this equation: x − 12 = 40?

A). 12 − x = 40

B). x over 2 = 14

C). x over 4 = 13

D). x +12 = −40

Answer 1

An expression for the length of the rectangle in terms of the width would be

Answer 2

To find which equation has the same solution for \( x \) as the equation \( x - 12 = 40 \), we first need to solve the original equation:

\[
x - 12 = 40
\]

Adding 12 to both sides gives:

\[
x = 40 + 12
\]

\[
x = 52
\]

Now we can check each option to see if it also results in \( x = 52 \):

A) \( 12 - x = 40 \)

Subtracting 12 from both sides:

\[
-x = 40 - 12
\]
\[
-x = 28
\]

Multiplying by -1:

\[
x = -28 \quad (\text{Not the same solution})
\]

B) \( \frac{x}{2} = 14 \)

Multiplying both sides by 2 gives:

\[
x = 14 \times 2
\]
\[
x = 28 \quad (\text{Not the same solution})
\]

C) \( \frac{x}{4} = 13 \)

Multiplying both sides by 4 gives:

\[
x = 13 \times 4
\]
\[
x = 52 \quad (\text{This is the same solution})
\]

D) \( x + 12 = -40 \)

Subtracting 12 from both sides gives:

\[
x = -40 - 12
\]
\[
x = -52 \quad (\text{Not the same solution})
\]

The equation that has the same solution for \( x \) as \( x - 12 = 40 \) is:

**C) \( \frac{x}{4} = 13 \)**.

Answer 3

To express the length of a rectangle in terms of its width, we typically need to have some relationship between the length and the width.

Let's denote:
- \( L \) as the length of the rectangle
- \( W \) as the width of the rectangle

A common relationship used is the area of the rectangle. If you know the area \( A \) of the rectangle, the formula for the area is given by:

\[
A = L \times W
\]

From this, you can solve for the length \( L \) in terms of the width \( W \):

\[
L = \frac{A}{W}
\]

If the problem provides a specific relationship or a different equation that relates length and width (like a perimeter constraint or ratio), please provide that, and we can derive the expression based on that relationship. Otherwise, the formula above is a standard way to express the length in terms of the width when the area is known.