Question

Mr. Andrews used a horizontal number line to illustrate an addition problem, as shown. The number line from -4 to 3 has a rightward arrow from -3 and three-fourths to 3 and a leftward arrow from 1 and a half to -3 and three-fourths. Which equation is represented by this figure?

Answer 1

The equation represented by the figure is
`\[ -3 (3)/(4) - 1 (1)/(2) + x = 3 \]`

How did we get the value?

To determine the equation represented by the given number line, let's analyze the information provided. The number line goes from -4 to 3 and has a rightward arrow from -3 and three-fourths to 3 and a leftward arrow from 1 and a half to -3 and three-fourths.

1. The rightward arrow from -3 and three-fourths to 3 suggests addition.

2. The leftward arrow from 1 and a half to -3 and three-fourths suggests subtraction.

Let's set up the equation:

`\[ -3 (3)/(4) + x - 1 (1)/(2) = 3 \]`

Combine the terms with
`\( x \)` on one side:

`\[ -3 (3)/(4) - 1 (1)/(2) + x = 3 \]`

To simplify the left side, find a common denominator (4 in this case):

`\[ -(15)/(4) - (6)/(4) + x = 3 \]`

Combine the fractions:

`\[ -(21)/(4) + x = 3 \]`

Now, add
`\( (21)/(4) \)` to both sides to solve for
`\( x \)`:

`\[ x = 3 + (21)/(4) \]`

Combine the terms on the right side:

`\[ x = (12)/(4) + (21)/(4) \]`

`\[ x = (33)/(4) \]`

So, the equation represented by the figure is
`\[ -3 (3)/(4) - 1 (1)/(2) + x = 3 \]` which simplifies to
`\[ x = (33)/(4) \]`