Equations, Inequalities, and Literals

Consider the following procedure Benji used to solve the given inequality:
Given

 $y-12\ <-\ \left(2y\ -\ 3\right)$  
1.  $y-12\ <-2y\ -\ 3$  
2.  $3y-12<-3$  
3.  $3y<15$  
4.  $y<5$  

• The first mistake was made in step 3 but the answer is correct.

• The first mistake was made in step 3 making the answer incorrect.

• The first mistake was made in step 1 making the answer incorrect

• The first mistake was made in step 1 but the answer is correct.

Which of the following are equivalent to

 $-x\ge-3$  ?

•  $x\ge-3$  

•  $x\ge3$  

•  $x\le-3$  

•  $x\le3$  

Tags

CCSS.6.EE.B.8

A small local company is trying to plan a holiday party for its employees. They will have to pay a $250 nonrefundable deposit and $12 per employee. The company's holiday party budget can not exceed $3000. Which of the following can be used to determine the number of employees attending the party. 

•  $12x\ +\ 250>3000$  

•  $3000\ -\ 12x\ \ge250$  

•  $12x\ +\ 250\le3000$  

•  $3000-250x\ =12$  

Tags

CCSS.7.EE.B.4B

Solve for y.

 $m\ =\frac{xyz}{4}$  

•  $y\ =\ 4m\ -xz$  

•  $y=m+4\ -\ xz$  

•  $y=\frac{4m}{xz}$  

•  $y=\frac{m+4}{xz}$  

Tags

CCSS.HSA.CED.A.4

Solve for a.

 $x=5a\ +7b$  

•  $a\ =\ \frac{x-7b}{5}$  

•  $a=\frac{x+7b}{5}$  

•  $a=5\left(-7b-x\right)$  

•  $a=\frac{x}{5}-7$  

Tags

CCSS.HSA.CED.A.4

Solve for h

V = πr²h for h

• V/(πr²) = h

• V - πr² = h

• V + πr² = h

• V/π = h

Tags

CCSS.HSA.CED.A.4

8x + 4y= 16 Solve for y.

• y = -8x + 16

• y = 2x -4

• y = -2x + 4

• y = -8x + 12

Tags

CCSS.6.EE.C.9

8x + 4y= 16 Solve for y.

• y = -8x + 16

• y = 2x -4

• y = -2x + 4

• y = -8x + 12

5x - y = 16

• -y = 5x + 16
• y = 5x + 16
• x = 5y - 16
• y = 5x - 16

Tags

CCSS.6.EE.C.9

Solve for l      $P=2\left(l+w\right)$

•  $l=\frac{2P}{w}$ 

•  $l=\frac{2w+P}{2}$ 

•  $l=p-\frac{w}{2}$ 

•  $l=\frac{P-2w}{2}$ 

Tags

CCSS.HSA.CED.A.4