One Step Equations and Properties of Equality

Mrs. Smith is helping Rohan solve this linear equation for x. Original equation: \(\frac{1}{2}\left(x+6\right)\ =\ -\frac{3}{2}x+5\) Step 1: \(\frac{1}{2}x+3\ =-\frac{3}{2}x+5\) Step 2: 2x + 3= 5 Step 3: 2x = 2 Step 4: x =1 Step 5: 2x = 2 Answer: x = 1 Which properties did she apply from step 1 to step 2?

• S1: Mult. poe

  S2: Add. poe

  S3: CLT

  S4: Division poe

• S1: Distributive prop

  S2: Subtract. poe

  S3: Add. poe

  S4: Division poe

• S1: Distributive prop

  S2: Add. poe

  S3: Subtract. poe

  S4: Division poe

• S1: Mult. poe

  S2: Subtract. poe

  S3: CLT

  S4: Division poe

Mr Hollar is solving an equation and moves from Step 1 to Step 2. Which property justifies the work between Step 1 and Step 2?

• Inverse Property of Multiplication

• Identity Property of Multiplication

• Multiplication Property of Equality

• Division Property of Equality

Move a property into each box of the reason column to justify each step.

f

b

h

d

Addition Property of Equality

Subtraction Property of Equality

Reflexive Property of Equality

Division Property of Equality

Multiplication Property of Equality

Commutative Property

Distributive Property

Associative Property

B=B

• Reflexive Property

• Symmetric Property

• Transitive Property

• Substitution Property

Identify the property of equality. If a = b and b = c, then a = c

• Transitive Property         

• Symmetric Property

• Reflexive Property

• Substitution Property

Jake earns $5 per hour mowing lawns. How many hours must he work to earn $40? Which equation would help you find the number of hours?

• 5 + x = 40

• 5 - x = 40

• x ÷ 5 = 40

• 5x = 40

What is the answer?

3x + 2 = -5x + 10

• x = 1

• x = -1

• x = 6

• x = -6

Answer explanation

If we add 5x to both sides, we get;

8x + 2 = 10.

Then we need to subtract 2 from both sides to get;

8x = 8.

Finally we divide both sides by what is attached to the x, which in this case is 8.

8x/8 = x and 8/8 = 1 so x=1

If I wanted to start to simplify this equation what would I do in order to get variables on one side and constants on the other?

• Move the 2x to the other side of the equation by adding it to both sides.

• Move the 6 to the other side of the equation by adding it to both side.

• Move the 2x to the other side of the equation by subtracting it from both sides.

• Move the 6 to the other side of the equation by subtracting it from both sides.

Answer explanation

If we move the 2x, then all terms with a variable will be on the right, and all constants will be on the left. Since the 2x is positive on the left, we want to do the opposite and subtract it from both sides.

What property did I use from step 1 to step 2?

• Distributive Property

• Combine like terms

• Addition Property of Equality

• Subtraction Property of Equality

Answer explanation

From step 1 to step 2 notice the parantheses go away. Tha tis because

Reorder the following based on which properties I used in solving the following equation;

• Distributive Property

• Combine Like Terms

• Subtraction Property of Equality

• Addition Property of equality

• Division Property of Equality

Answer explanation

To get rid of the parentheses w use the distributive property.

Then to simplify each side, we combine like terms.

Next the variable terms were all moved to the right side of the equation. The 4x was subtracted from both sides, hence the subtraction property of equality.

Next, we needed to get the constants on the opposite side of the equation, so we added 5 to both sides, hence the addition property of equality.

Finally we used the division prperty and divided both sides by what was attached to the x, which in this case was a 3. We used the division property of equality to get an answer of 1/3 = x.