Algebraic Properties Solving Equations

Translate into an algebraic expression.

Two times the difference of a number and four is two. 

• 2x-4=2

• 2(x-4)=2

• 2-x+4=2

Ariel needs to solve this equation for x. What would be the best first step Ariel could make to solve the equation?

• Add 7 to both sides of the equation

• Divide both sides of the equation by 3

• Subtract 7 from both sides of the equation

• Multiply both sides of the equation by 3

Karen solve an equation incorrectly as shown below. Given: 4(x + 1) - 3(x -2) = 11 Step 1: 4x + 4 - 3x + 6 = 11 Step 2: 4x - 3x + 4 + 6 = 11 Step 3: x + 10 = 11 Step 4: x + 10 + 10 = 11 + 10 Answer: x = 21

• From given to step 1

• From step 1 to step 2

• From step 2 to step 3

• From step 3 to step 4

Jared solved the equation shown below. Given: 5(x + 1) - 3(x -2) = 13 Step 1: 5x + 5 - 3x + 6 = 13 Step 2: 5x - 3x + 5 + 6 = 13 Step 3: 2x + 11 = 13 Step 4: 2x + 11 - 11 = 13 - 11 Step 5: 2x = 2 Answer: x = 1 Which properties did he apply from step 1 to step 2?

• Associative pro

• Distributive property

• Subtraction property

• Commutative property

Lisa completes the steps for solving 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 he 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

Jill solved the equation below. 2\left(x\ -1\right)\ =\ x\ +12 2x\ -\ 2\ =\ x+12 x-2=\ 12 x=14 She applied three properties of equality: I. Addition property of equality, II. Subtraction property of equality and III. Distributive property. In which order did Jill use the properties?

• I, II, III

• III, I, II

• III, II, I

• I, III, II

Understanding these properties is essential for solving algebraic ___

Why is identifying algebraic properties crucial in mathematical equations?

• To simplify complex expressions

• To memorize formulas

• To learn geometry

• To study history of mathematics

What is a key skill in algebra?

• Solving equations

• Reading novels

• Cooking recipes

• Playing video games

What is the main focus of algebra?

• Geometry

• Calculus

• Solving equations with variables

• Biology