Linear Equations, Inequalities & Systems Assessment

Select all equations that are equivalent to $\frac{\left(5x+6\right)}{2}=3-\left(4x+12\right)$  

•  $5x+6=3-\left(4x+12\right)$  

•  $\frac{\left(5x+6\right)}{2}=-4x-9$  

•  $\frac{5}{2}x+3=3-\left(4x+12\right)$  

•  $\frac{\left(5x+6\right)}{2}=-4x+15$  

•  $5x+6=-8x-18$  

Tags

CCSS.8.EE.C.7A

A phone company charges a base fee of $12 per month plus an additional charge per minute. The monthly phone cost C can be represented by this equation: $C=12+a\cdot m$ , where a is the additional charge per minute, and m is the number of minutes used.Which equation can be used to find the number of minutes a customer used, m, if we know a and C? 

•  $m=\frac{\left(C-12\right)}{a}$  

•  $m=\left(C-12\right)-a$  

•  $m=C-12a$  

•  $m=\frac{C}{a}-12$  

Tags

CCSS.HSA.CED.A.4

Tickets to the zoo cost $12 for adults and $8 for children. The school has a budget of $240 for the field trip. An equation representing the budget for the trip is $240=12x+8y$ . Here is a graph of this equation.

• If no adult chaperones were needed, 30 students could go to the zoo.

• If ten students go to the zoo, then 15 adults can go.

• If 16 adults go to the zoo, then 6 students can go.

Tags

CCSS.HSA.REI.C.6

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.10

CCSS.HSA.SSE.A.1

Solve the system of equations without graphing. Show your reasoning. Use substitution or elimination.
 $2y=x-4$ 
 $4x+3y=5$  

•  $y=-1\ and\ x=2$  

•  $y=-1\ and\ x=6$  

•  $y=1\ and\ x=-6$  

•  $y=-1\ and\ x=-2$  

•  $y=1\ and\ x=-2$  

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Consider the inequality $\frac{x+3}{6}>\frac{x}{4}+1$ . Which value of x is a solution to the inequality?

•  $x=-10$  

•  $x=-6$  

•  $x=6$  

•  $x=10$  

Tags

CCSS.6.EE.B.5

 $y>\frac{4}{3}x-4$  Graph the solution to the inequality

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Tags

CCSS.HSA.REI.D.12

A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per week. His goal is to make at least $300 per week. Which system of inequalities models the situations, if y=hours gardening and x= hours mowing?

• $20\ge x+y$ $300\le15x+20y$

• $20\le x+y$ $300\ge15x+20y$

• $20\ge15x+20y$ $300\le x+y$

• $20\ge x+15y$ $300\le x+20y$

Tags

CCSS.HSA.REI.D.12

CCSS.HSA.REI.C.6

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.D.11

A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per week. His goal is to make at least $300 per week. The situation can be modeled the following system of inequalities:
 $y\le-x+20$  
 $y\ge-\frac{3}{4}x+15$  
Which graph shades the region that shows all the points that represents the number of hours the student can work at each job and meet his goal?

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Tags

CCSS.HSA.REI.D.12

 $4x+5y<20$  Graph the solution to the inequality

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Tags

CCSS.HSA.REI.D.12

Graph the solution to this system of inequalities
 $3x-5y\le15$  

 $y>-\frac{2}{3}x+1$  

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Tags

CCSS.HSA.REI.D.12