Solving and Justifying Solutions to Equations

Sally correctly solved an equation and got w = 15 as her answer. What type of solution does this equation have?

• One Solution

• No Solution

• Infinite Solutions

Lisa correctly solved an equation and got 5 = 1 as her answer. What type of solution does this equation have?

• One Solution

• No Solution

• Infinite Solutions

Find the Error
What error did the student make when solving the equation:
1/5x + 6 = 3/5x + 5
1x + 6 = 3x + 5
-2x + 6 = 5
-2x = -1
x = 1/2

• The student found an incorrect common denominator

• The student did not multiply all terms by the common denominator

• The student did not use opposite operations appropriately

• The student did not correctly eliminate the variable from one side of the equation

Step 1) GIVEN

Step 2) ​ (a)  

Step 3) ​ COMBINE LIKE TERMS

Step 4) SUBTRACTION PROPERTY

Step 5) ​ (b)  

Step 6) ​ DIVISION PROPERTY

Step 7: SIMPLIFY

• DISTRIBUTIVE PROPERTY

• COMBINE LIKE TERMS

• MULTIPLICATION PROPERTY

• ADDITION PROPERTY

• SUBTRACTION PROPERTY

• DIVISION PROPERTY

• No Solution

• Infinite Solutions

Sarah incorrectly solved the equation -6(7n+7)=-294 as shown.

Step 1: -6(7n + 7) = -294
Step 2: -42n - 42 = -294
Step 3: -42n = -336
Step 4: n = 8
Between which two steps did Sarah make a mistake?

• Step 1 and Step 2

• Step 2 and Step 3

• Step 3 and Step 4

Peter incorrectly solved the equation 86=-5(-6+2x)+3x as shown.

Step 1: 86 = -5(-6 + 2x) + 3x
Step 2: 86 = 30 + 10x + 3x
Step 3: 86 = 30 + 13x
Step 4: 56 = 13x
Step 5: 4.3 = x

• Step 1 and Step 2

• Step 2 and Step 3

• Step 3 and Step 4

• Step 4 and Step 5

Which justification would be used for STEP 3?

• Addition Property of Equality

• Subtraction Property of Equality

• Combine Like Terms

• Division Property of Equality

• Distributive Property

Which justification would be used for STEP 4?

• Addition Property of Equality

• Subtraction Property of Equality

• Combine Like Terms

• Division Property of Equality

• Distributive Property

Given the equation: 14x - 12 = 3x + 5 + px What value of p makes the equation have no solution?

• 11

• 14

• 12

• 1