Question

understand analysis what do you know? what is happening in the problem? what is the variable? what does the variable represent? what other values are important? what do they represent? what operation is being used? what are you looking for? what is unknown? plan devise a plan choose a strategy choose a strategy look for a pattern draw a picture or diagram make a list or table solve a simpler problem use a guess and check write an equation use a formula remember a related problem how will you solve the problem? what strategy will you use to visualize the problem? what is the inverse operation you will use to solve? to solve the problem, i will write an equation or inequality to represent the situation solve carry out the plan implementation what operation is being used with the variable? what inverse operation will you use to isolate the variable? did you do the inverse on both sides of the equal sign? is the variable isolated? did you check your answer? check justify your answer reflection what is the solution? what is the meaning of your solution? how do you know your solution is correct? inequality used to solve the inequality and name the property of 3. ( m - 15 < 81 ) 4. (partially visible) 5. ( 81 < 27a ) 6. ( 6.8 + d geq 11.4 ) solve the inequality. graph the solution. 7. ( 1 leq k - \frac{1}{4} ) (with number line from 0 to 5) 8. the owner of a garden store is hiring additional employees for the summer. he already employs 14 people and wants to have a total of no more than 19 employees. what is an inequality that represents how many employees, ( e ), the owner can hire? what is the solution? 9. nicolas is making bracelets for his friends. he needs 12 beads for each bracelet, and he has 156 beads. what inequality represents how many

Explanation:

Step1: Solve $m - 15 < 81$

Add 15 to both sides:
$m - 15 + 15 < 81 + 15$
$m < 96$

Step2: Solve $81 < 27a$

Divide both sides by 27:
$\frac{81}{27} < \frac{27a}{27}$
$3 < a$ or $a > 3$

Step3: Solve $6.8 + p \geq 11.4$

Subtract 6.8 from both sides:
$6.8 + p - 6.8 \geq 11.4 - 6.8$
$p \geq 4.6$

Step4: Solve $1 \leq k - \frac{3}{4}$

Add $\frac{3}{4}$ to both sides:
$1 + \frac{3}{4} \leq k - \frac{3}{4} + \frac{3}{4}$
$\frac{4}{4} + \frac{3}{4} \leq k$
$k \geq \frac{7}{4} = 1.75$
To graph: Draw a closed circle at $1.75$ on the number line, shade to the right.

Step5: Set up garden employee inequality

Let $e$ = number of new employees. Total employees: $14 + e$, which is no more than 19:
$14 + e \leq 19$
Subtract 14 from both sides:
$e \leq 19 - 14$
$e \leq 5$

Step6: Set up bracelet inequality

Let $b$ = number of bracelets. Beads used: $12b$, which is ≤ total beads 156:
$12b \leq 156$
Divide both sides by 12:
$b \leq \frac{156}{12}$
$b \leq 13$

Answer:

1. $m < 96$
2. $a > 3$
3. $p \geq 4.6$
4. $k \geq \frac{7}{4}$; Graph: Closed circle at $1.75$, shade right
5. Inequality: $14 + e \leq 19$; Solution: $e \leq 5$
6. Inequality: $12b \leq 156$; Solution: $b \leq 13$