Answer :
To determine which value of [tex]\( x \)[/tex] makes the rational expression [tex]\(\frac{10-z}{7+x}\)[/tex] undefined, we need to focus on the denominator. A rational expression is undefined if its denominator is equal to zero.
Step 1: Set the denominator equal to zero.
[tex]\[ 7 + x = 0 \][/tex]
Step 2: Solve for [tex]\( x \)[/tex].
- Subtract 7 from both sides of the equation to isolate [tex]\( x \)[/tex].
[tex]\[ x = -7 \][/tex]
The expression becomes undefined when [tex]\( x = -7 \)[/tex].
Therefore, the value of [tex]\( x \)[/tex] that makes the expression [tex]\(\frac{10-z}{7+x}\)[/tex] undefined is [tex]\( x = -7 \)[/tex].
So, the correct answer is option C: -7.
Step 1: Set the denominator equal to zero.
[tex]\[ 7 + x = 0 \][/tex]
Step 2: Solve for [tex]\( x \)[/tex].
- Subtract 7 from both sides of the equation to isolate [tex]\( x \)[/tex].
[tex]\[ x = -7 \][/tex]
The expression becomes undefined when [tex]\( x = -7 \)[/tex].
Therefore, the value of [tex]\( x \)[/tex] that makes the expression [tex]\(\frac{10-z}{7+x}\)[/tex] undefined is [tex]\( x = -7 \)[/tex].
So, the correct answer is option C: -7.
