MATH 8 Mod 4 Lessons 1-9

Ofelia has a certain amount of money.  She spends $12, and then she has 1/5  of the original amount left. 

Choose 1 correct equation:

•  $12=\frac{1}{5}x$  

•  $x-12=\frac{1}{5}x$  

•  $x-12=\frac{1}{5}$  

Two consecutive integers have a sum of 234.

Choose 2 correct equations.

• $x+x+1=234$

• $2x=234$

• $x+\left(x+1\right)=234$

Subtract seven more than a number from 5 times the same number to get zero.

Choose 1 correct equation:

•  $5x-x+7=0$ 

•  $\left(x+7\right)-5x=0$ 

•  $5x-\left(x+7\right)=0$ 

When you square five times a number, you get three more than the number.

Choose 1 correct equation:

• $5x^2=3+x$

• $\left(5x\right)^2=3+x$

Monica had some cookies. She gave seven to her sister. Then, she divided the remainder into two halves, and she still had five cookies left.

Choose all correct equations:

• $\frac{\left(x-7\right)}{2}=5$

• $\frac{1}{2}\left(x-7\right)=5$

• $0.5\left(x-7\right)=5$

Write an expression or equation:

Seven subtracted from five times a number, and then the difference added to nine times a number

• $\left(7-5x\right)+9x$

• $\left(5x-7\right)+9x$

Is -3 a solution to the equation 3x-5=4+2x?

Which statement below is INCORRECT?

• -3 is a solution because when I replace x with -3 it makes the left hand side of the equation equal to the right hand side

• -3 is not a solution to the equation because when I solve the equation I get x = 9.

• -3 is not a solution because when I replace x with -3 it makes the left hand side equal to -14 and the right hand side equal to -2.

 $16-\frac{1}{2}x=\frac{3}{4}x+17$  

 Does x = 12 satisfy this equation?

• 
   $16-\frac{1}{2}\cdot12=\frac{3}{4}\cdot12+17$  
   $16-6\ =\ 9\ +\ 17$  
  

•  $16-\frac{1}{2}\cdot12\ne\frac{3}{4}\cdot12+17$  
  
   $16-6\ne9+17$  
  

 $5\left(3x+4\right)-2x=7x-3\left(-2x+11\right)$  

Choose all that are correct.

• The first step to solve is to distribute:
   $5\cdot3x+5\cdot4-2x=7x+-3\left(-2x\right)-3\left(11\right)$  
  

• The result of distributing and combining like terms is:
   $13x+20=13x-33$  
  

• There is NO SOLUTION to this equation

 $x-9=\frac{3}{5}x$  

Choose all possible first steps.

• A possible first step is to subtract x from both sides:
   $-9=\frac{3}{5}x-x$  
  

• A possible first step is to change 3/5 to a decimal:
   $x-9=0.6x$  
  

• A possible first step is to subtract 9 from both sides:

  
   $x-9-9=\frac{3}{5}x-9$