Answer :
To determine which expression is equivalent to [tex]\( |4 - 3| \)[/tex], we need to follow these steps:
1. Evaluate the expression inside the modulus:
[tex]\[ 4 - 3 = 1 \][/tex]
2. Apply the modulus operation:
[tex]\[ |1| = 1 \][/tex]
Now, let’s compare the value [tex]\( 1 \)[/tex] with the given choices to identify the correct one:
1. [tex]\( 1 \)[/tex]
2. [tex]\( \sqrt{7} \)[/tex]
3. [tex]\( 5i \)[/tex]
4. [tex]\( 5 \)[/tex]
We see that:
- The first option is [tex]\( 1 \)[/tex], which matches our evaluated value.
- The second option, [tex]\( \sqrt{7} \)[/tex], is a real number greater than 2 but does not match [tex]\( 1 \)[/tex].
- The third option, [tex]\( 5i \)[/tex], is an imaginary number and thus does not match [tex]\( 1 \)[/tex].
- The fourth option, [tex]\( 5 \)[/tex], is a real number greater than 1 and cannot be [tex]\( 1 \)[/tex].
Thus, the expression equivalent to [tex]\( |4 - 3| \)[/tex] is [tex]\( 1 \)[/tex].
Therefore, the correct option is:
[tex]\[ \boxed{1} \][/tex]
1. Evaluate the expression inside the modulus:
[tex]\[ 4 - 3 = 1 \][/tex]
2. Apply the modulus operation:
[tex]\[ |1| = 1 \][/tex]
Now, let’s compare the value [tex]\( 1 \)[/tex] with the given choices to identify the correct one:
1. [tex]\( 1 \)[/tex]
2. [tex]\( \sqrt{7} \)[/tex]
3. [tex]\( 5i \)[/tex]
4. [tex]\( 5 \)[/tex]
We see that:
- The first option is [tex]\( 1 \)[/tex], which matches our evaluated value.
- The second option, [tex]\( \sqrt{7} \)[/tex], is a real number greater than 2 but does not match [tex]\( 1 \)[/tex].
- The third option, [tex]\( 5i \)[/tex], is an imaginary number and thus does not match [tex]\( 1 \)[/tex].
- The fourth option, [tex]\( 5 \)[/tex], is a real number greater than 1 and cannot be [tex]\( 1 \)[/tex].
Thus, the expression equivalent to [tex]\( |4 - 3| \)[/tex] is [tex]\( 1 \)[/tex].
Therefore, the correct option is:
[tex]\[ \boxed{1} \][/tex]
