Let's solve the inequality step-by-step.
First, simplify the left-hand side of the inequality:
[tex]\[
3 \cdot 13 + 2 \cdot 4 \leq 46
\][/tex]
Calculate [tex]\(3 \cdot 13\)[/tex]:
[tex]\[
3 \cdot 13 = 39
\][/tex]
Calculate [tex]\(2 \cdot 4\)[/tex]:
[tex]\[
2 \cdot 4 = 8
\][/tex]
Now combine these results on the left side:
[tex]\[
39 + 8 = 47
\][/tex]
So, the inequality becomes:
[tex]\[
47 \leq 46
\][/tex]
Next, let's determine whether this statement is true or false. Is 47 less than or equal to 46? Clearly:
[tex]\[
47 \not\leq 46
\][/tex]
Therefore, the given statement is false.
To summarize:
The inequality simplifies to [tex]\(47 \leq 46\)[/tex].
Since [tex]\(47\)[/tex] is not less than or equal to [tex]\(46\)[/tex], the given statement is false.
