Question

17.for problems 18-20, write an inequality that swaps the positions of the variable and the number but has the same solutions.18. $15 < t$19. $-4.5 \geq x$20. $c \leq 90$for problems 21-24, define a variable and write an inequality that represents the situation.21. only children 12 years or younger can order from the kids menu at vics diner.22. the planning committee wants at least 40 students to attend the school dance.23. ava may play video games for no more than one and a half hours a day.

Explanation:

Step1: Swap variable and number, reverse inequality

For $15 < t$: Reverse the sign and swap terms.
$t > 15$

Step2: Swap variable and number, reverse inequality

For $-4.5 \geq x$: Reverse the sign and swap terms.
$x \leq -4.5$

Step3: Swap variable and number, reverse inequality

For $c \leq 90$: Reverse the sign and swap terms.
$90 \geq c$

Step4: Define variable, write inequality

Let $a$ = child's age. Max age is 12.
$a \leq 12$

Step5: Define variable, write inequality

Let $s$ = number of students. Need at least 40.
$s \geq 40$

Step6: Define variable, write inequality

Let $g$ = daily game time (hours). Max 1.5.
$g \leq 1.5$

Answer:

1. $t > 15$
2. $x \leq -4.5$
3. $90 \geq c$
4. Let $a$ = a child's age; $a \leq 12$
5. Let $s$ = number of students; $s \geq 40$
6. Let $g$ = daily video game time (hours); $g \leq 1.5$