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The length of a rectangle is 4 units shorter than half the width. If the length of the rectangle is 18 units, which equation can be used to find [tex]\( w \)[/tex], the width of the rectangle?

A. [tex]\( 18 = \frac{w}{2} - 4 \)[/tex]
B. [tex]\( 18 = 4 - \frac{w}{2} \)[/tex]
C. [tex]\( 18 - 4 = \frac{w}{2} \)[/tex]
D. [tex]\( 18 - \frac{w}{2} = 4 \)[/tex]


Sagot :

To determine which equation can be used to find [tex]\( w \)[/tex], the width of the rectangle, let's start by understanding the relationship provided in the problem:

- The length of the rectangle is 4 units shorter than half the width.

In mathematical terms:

[tex]\[ \text{Length} = \frac{w}{2} - 4 \][/tex]

Given that the length is 18 units:

[tex]\[ 18 = \frac{w}{2} - 4 \][/tex]

We can solve this equation step-by-step to find [tex]\( w \)[/tex]:

1. Starting from:
[tex]\[ 18 = \frac{w}{2} - 4 \][/tex]

2. To isolate [tex]\( \frac{w}{2} \)[/tex], we add 4 to both sides of the equation:
[tex]\[ 18 + 4 = \frac{w}{2} \][/tex]

3. Simplifying the left side:
[tex]\[ 22 = \frac{w}{2} \][/tex]

4. Finally, to solve for [tex]\( w \)[/tex], we multiply both sides by 2:
[tex]\[ w = 44 \][/tex]

Now, looking back at the given equations, we see that the one that matches the step we performed (adding 4 to both sides) is:

[tex]\[ 18 - 4 = \frac{w}{2} \][/tex]

Therefore, the equation that can be used to find [tex]\( w \)[/tex] is:

[tex]\[ 18 - 4 = \frac{w}{2} \][/tex]

This corresponds to option 3.