Question

solving an inequality solve the inequality. graph the solution. 24. $9x - 4x + 4 \geq 36 - 12$ 25. $3d - 7d + 2.8 < 5.8 - 27$ 26. mp modeling real life a cave explorer is at an elevation of $-38$ feet. the explorer starts moving at a rate of $-12$ feet per minute. write and solve an inequality that represents how long it will take the explorer to reach an elevation deeper than $-200$ feet.

Explanation:

Step1: Simplify left/right sides (Q24)

$9x-4x+4 = 5x+4$; $36-12=24$
Inequality: $5x+4\geq24$

Step2: Isolate variable term (Q24)

$5x\geq24-4$
$5x\geq20$

Step3: Solve for x (Q24)

$x\geq\frac{20}{5}$
$x\geq4$

Step4: Simplify left/right sides (Q25)

$3d-7d+2.8=-4d+2.8$; $5.8-27=-21.2$
Inequality: $-4d+2.8<-21.2$

Step5: Isolate variable term (Q25)

$-4d<-21.2-2.8$
$-4d<-24$

Step6: Solve for d (Q25)

$d>\frac{-24}{-4}$ (reverse inequality sign)
$d>6$

Step7: Define variable & inequality (Q26)

Let $t$ = time in minutes.
Inequality: $-38-12t<-200$

Step8: Isolate variable term (Q26)

$-12t<-200+38$
$-12t<-162$

Step9: Solve for t (Q26)

$t>\frac{-162}{-12}$ (reverse inequality sign)
$t>13.5$

Answer:

1. $x\geq4$ (Graph: Closed circle at 4, shade right)
2. $d>6$ (Graph: Open circle at 6, shade right)
3. $t>13.5$; The explorer takes more than 13.5 minutes to reach elevation deeper than -200 feet.