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Suppose we have [tex]\( \overline{XZ} \)[/tex], with [tex]\( Y \)[/tex] between [tex]\( X \)[/tex] and [tex]\( Z \)[/tex].

Let [tex]\( XY = 4x + 4 \)[/tex], [tex]\( YZ = 5x \)[/tex], and [tex]\( XZ = 58 \)[/tex]. Find the value of [tex]\( YZ \)[/tex].

[tex]\[ YZ = \][/tex]



Answer :

GinnyAnswer
To solve for [tex]\( YZ \)[/tex] given the information:

1. Identify the given expressions:
- [tex]\( XY = 4x + 4 \)[/tex]
- [tex]\( YZ = 5x \)[/tex]
- [tex]\( XZ = 58 \)[/tex]

2. Use the fact that the total distance [tex]\( XZ \)[/tex] is the sum of [tex]\( XY \)[/tex] and [tex]\( YZ \)[/tex]:
[tex]\[ XZ = XY + YZ \][/tex]

3. Substitute the expressions for [tex]\( XY \)[/tex] and [tex]\( YZ \)[/tex] into the equation [tex]\( XZ = 58 \)[/tex]:
[tex]\[ 58 = (4x + 4) + 5x \][/tex]

4. Combine like terms:
[tex]\[ 58 = 4x + 4 + 5x \quad \Rightarrow \quad 58 = 9x + 4 \][/tex]

5. Isolate [tex]\( x \)[/tex] by first subtracting 4 from both sides of the equation:
[tex]\[ 58 - 4 = 9x \quad \Rightarrow \quad 54 = 9x \][/tex]

6. Solve for [tex]\( x \)[/tex] by dividing both sides by 9:
[tex]\[ x = \frac{54}{9} \quad \Rightarrow \quad x = 6 \][/tex]

7. Substitute [tex]\( x = 6 \)[/tex] back into the expression for [tex]\( YZ \)[/tex]:
[tex]\[ YZ = 5x \quad \Rightarrow \quad YZ = 5 \cdot 6 \quad \Rightarrow \quad YZ = 30 \][/tex]

So, the value of [tex]\( YZ \)[/tex] is:
[tex]\[ YZ = 30 \][/tex]

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