Solving Equation Practice (Math 8)

Solving Equation Practice (Math 8)

Get out your scratch paper and a calculator.

Can you find the error?

The next slide will show the error.

Correction

• The error was in the division

• The correct answer is x = 1/2 or x = 0.5

Multiple Choice

Solve the equation below:

 $5y+2=3y+10$ 

Work this equation: Hint move the smaller coefficient (number with the variable).

•  $y=4$  

•  $y=8$  

•  $y=-4$  

•  $y=2$  

Equations with variables on both sides of the equals sign

• Move the smaller variable first.

• Do you understand what they are doing on each step?

Multiple Choice

What step has the error?

• Step A

• Step B

• Step C

• Step D

Mistake was in Step B

• They forgot to pull down the negative sign with the 12

• 3x + 9 = -12 Should be the Step B

Special Cases

Usually equations have 1 solution.

However, equations are special cases when there is NO SOLUTION or INFINITE solutions

Another example of No Solution

Another example of Infinite Solutions

Multiple Choice

Solve: (hint: distribute)

 $4y+12\ =\ 2\left(2y+6\right)$  

• no solution
  

• infinite solution
  

•  $y=0$  

Multiple Choice

Solve:

 $-2\left(3y+1\right)=y\ -\ 2\$  

•  $y=0$  

•  $y=-1$  

• No Solution
  

• Infinite Solution
  

Multiple Choice

Solve:

 $\frac{1}{3}\left(6y+3\right)=3+2y$  

• infinite solution
  

• no solution
  

•  $y=2$  

Can you find the error?

The next slide will show the error.

The error occurred on the first step.

• They did not distribute correctly

• Correct answer is x = -17

Multiple Choice

Carl solved a linear equation and the last line of his work was: 3 = 3 Which statement best describes the solution to the equation Carl was solving?

• The solution is 3

• There is no solution

• The are infinite solutions

Multiple Choice

Which equation has NO solution?

• $6y+8=2\left(3y+4\right)$

• $5w+7=3+5w$

• $3y+3+y=19$

Multiple Choice

Solve:Combine Like Terms First

 $2y+6+y=-12$  

•  $y=-5$  
  

•  $y=6$  
  

•  $y=-8$  

  
  

•  $y=-6$  

Multiple Choice

Jack solved a linear equation and the last line of his work was: 8 = 12 Which statement best describes the solution to the equation Jack was solving?

• The solution is 3

• There is no solution

• The are infinite solutions

Multiple Choice

Solve:

 $6m+10=m+40$  

•  $m=6$  

•  $m=5$  

•  $m=8$  

Multiple Choice

Solve:  $-5w+8=-8w+5$  

•  $w=-3$  

•  $w=1$  

•  $w=-1$  

2nd Chance

If you need to go back and correct (OR COMPLETE) the equation sort, this is your chance.

Equations are getting stronger

The key is that you need to work them out on paper.