To determine which of the values satisfy the inequality [tex]\( 2x - 3 \leq 10 \)[/tex], we need to verify each value by substituting it into the inequality and checking if the result holds true. Let's proceed with each provided value step-by-step.
1. Check [tex]\( x = 26 \)[/tex]:
[tex]\[
2(26) - 3 \leq 10
\][/tex]
[tex]\[
52 - 3 \leq 10
\][/tex]
[tex]\[
49 \leq 10 \quad \text{(False)}
\][/tex]
Since [tex]\( 49 \)[/tex] is not less than or equal to [tex]\( 10 \)[/tex], [tex]\( x = 26 \)[/tex] is not a solution.
2. Check [tex]\( x = 7 \)[/tex]:
[tex]\[
2(7) - 3 \leq 10
\][/tex]
[tex]\[
14 - 3 \leq 10
\][/tex]
[tex]\[
11 \leq 10 \quad \text{(False)}
\][/tex]
Since [tex]\( 11 \)[/tex] is not less than or equal to [tex]\( 10 \)[/tex], [tex]\( x = 7 \)[/tex] is not a solution.
3. Check [tex]\( x = 5 \)[/tex]:
[tex]\[
2(5) - 3 \leq 10
\][/tex]
[tex]\[
10 - 3 \leq 10
\][/tex]
[tex]\[
7 \leq 10 \quad \text{(True)}
\][/tex]
Since [tex]\( 7 \)[/tex] is less than or equal to [tex]\( 10 \)[/tex], [tex]\( x = 5 \)[/tex] is a valid solution.
4. Check [tex]\( x = 10 \)[/tex]:
[tex]\[
2(10) - 3 \leq 10
\][/tex]
[tex]\[
20 - 3 \leq 10
\][/tex]
[tex]\[
17 \leq 10 \quad \text{(False)}
\][/tex]
Since [tex]\( 17 \)[/tex] is not less than or equal to [tex]\( 10 \)[/tex], [tex]\( x = 10 \)[/tex] is not a solution.
By evaluating each of the given values, we find that the only value that satisfies the inequality [tex]\( 2x - 3 \leq 10 \)[/tex] is [tex]\( x = 5 \)[/tex].
Therefore, the solution is:
[tex]\[
x = 5
\][/tex]
