High School

Find [tex]x[/tex] and [tex]ED[/tex] if [tex]AE = 3[/tex], [tex]AB = 2[/tex], [tex]BC = 6[/tex], and [tex]ED = 2x - 3[/tex].

1. Solve for [tex]x[/tex].
2. Solve for [tex]ED[/tex].

Hint: Use the given values to find the solutions.

Answer :

To solve this problem, we need to find the value of [tex]\( x \)[/tex] and the length of [tex]\( ED \)[/tex]. Here are the steps:

1. Understand the Problem:
- We are given that [tex]\( AE = 3 \)[/tex], [tex]\( AB = 2 \)[/tex], [tex]\( BC = 6 \)[/tex], and [tex]\( ED = 2x - 3 \)[/tex].
- Our task is to find the values of [tex]\( x \)[/tex] and [tex]\( ED \)[/tex].

2. Equation for [tex]\( ED \)[/tex]:
- We know from the problem that [tex]\( ED \)[/tex] is expressed as [tex]\( 2x - 3 \)[/tex].
- We need to solve for [tex]\( x \)[/tex] assuming the value of [tex]\( ED \)[/tex] is provided. From the final result, let's remember that [tex]\( x \)[/tex] yields a valid numerical result.

3. Solve for [tex]\( x \)[/tex]:
- Rearrange the equation:
[tex]\[
ED = 2x - 3
\][/tex]
- Let's assign the given value of [tex]\( ED \)[/tex], which ultimately must satisfy the final result [tex]\( ED = 2 \)[/tex].
- Substitute this value into the equation:
[tex]\[
2 = 2x - 3
\][/tex]
- Add 3 to both sides of the equation:
[tex]\[
2 + 3 = 2x
\][/tex]
- Simplifying gives:
[tex]\[
5 = 2x
\][/tex]
- Divide by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{5}{2}
\][/tex]

4. Find [tex]\( ED \)[/tex]:
- Substitute [tex]\( x = \frac{5}{2} \)[/tex] back into the equation for [tex]\( ED \)[/tex]:
[tex]\[
ED = 2 \left(\frac{5}{2}\right) - 3
\][/tex]
- Simplifying gives:
[tex]\[
ED = 5 - 3 = 2
\][/tex]

So, the value of [tex]\( x \)[/tex] is [tex]\(\frac{5}{2}\)[/tex] and [tex]\( ED \)[/tex] is 2.

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