Solve Equations Using the Subtraction and Addition Properties of Equality Quiz
The question sheet
Reveal any answer as you study-
What is a solution of an equation?
- A value that makes a true statement
- The largest variable value
- Any number in the equation
- The coefficient of the variable
Reveal answer
Answer: A value that makes a true statement
Source evidence
PDF page 212: A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.
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To determine if a number is a solution, what is the first step?
- Substitute the number for the variable
- Subtract from both sides
- Add the same quantity
- Simplify only the left side
Reveal answer
Answer: Substitute the number for the variable
Source evidence
PDF page 212: Step 1. Substitute the number in for the variable in the equation. Step 2. Simplify the expressions on both sides of the equation. Step 3. Determine whether the resulting equation is true (the left side is equal to the right side)
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After substituting, if the resulting equation is true, then the number is:
- Not a solution
- A solution
- A coefficient
- A variable
Reveal answer
Answer: A solution
Source evidence
PDF page 212: Step 1. Substitute the number in for the variable in the equation. Step 2. Simplify the expressions on both sides of the equation. Step 3. Determine whether the resulting equation is true (the left side is equal to the right side)
PDF page 212: ◦ If it is true, the number is a solution.
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According to the Subtraction Property of Equality, if a = b, then:
- a + c = b − c
- a − c = b + c
- a − c = b − c
- a = b − c
Reveal answer
Answer: a − c = b − c
Source evidence
PDF page 214: If a = b, then a − c = b − c
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What is the goal when solving these equations?
- To isolate the variable on one side
- To remove all numbers
- To add counters
- To multiply both sides
Reveal answer
Answer: To isolate the variable on one side
Source evidence
PDF page 214: Our model has given us an idea of what we need to do to solve one kind of equation. The goal is to isolate the variable by itself on one side of the equation. To solve equations such as these mathematically, we use the Subtraction Property of Equality.
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To solve y + 37 = −13, what do you do to each side?
- Add 37
- Multiply by 37
- Subtract 37
- Divide by 37
Reveal answer
Answer: Subtract 37
Source evidence
PDF page 214: To get y by itself, we will undo the addition of 37 by using the Subtraction Property of Equality.
PDF page 214: Subtract 37 from each side to ‘undo’ the addition. Simplify. Check: Substitute y = −50
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What is the solution to y + 37 = −13?
- y = −24
- y = −50
- y = 24
- y = 50
Reveal answer
Answer: y = −50
Source evidence
PDF page 214: Subtract 37 from each side to ‘undo’ the addition. Simplify. Check: Substitute y = −50
PDF page 214: Since y = −50 makes y + 37 = −13 a true statement, we have the solution to this equation.
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To solve a − 28 = −37, which property is used?
- Commutative Property
- Addition Property of Equality
- Subtraction Property of Equality
- Distributive Property
Reveal answer
Answer: Addition Property of Equality
Source evidence
PDF page 215: EXAMPLE 2.3 Solve: a − 28 = −37. Solution
PDF page 215: Add 28 to each side to ‘undo’ the subtraction. Simplify. Check: Substitute a = −9
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What is the solution to a − 28 = −37?
- a = −65
- a = 65
- a = 9
- a = −9
Reveal answer
Answer: a = −9
Source evidence
PDF page 215: The solution to a − 28 = −37 is a = −9.
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To solve x − 5 = 8, how do you undo the subtraction?
- Multiply both sides by 5
- Add the number to both sides
- Subtract 5 from both sides
- Divide both sides by 5
Reveal answer
Answer: Add the number to both sides
Source evidence
PDF page 214: What happens when an equation has a number subtracted from the variable, as in the equation x − 5 = 8 ? We use another property of equations to solve equations where a number is subtracted from the variable. We want to isolate the variable, so to ‘undo’ the subtraction we will add the number to both sides. We use the Addition Property of Equality.
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What should you always do before trying to isolate the variable?
- Check the answer
- Simplify as much as possible
- Add counters
- Translate to English
Reveal answer
Answer: Simplify as much as possible
Source evidence
PDF page 216: In the previous examples, we were able to isolate the variable with just one operation. Most of the equations we encounter in algebra will take more steps to solve. Usually, we will need to simplify one or both sides of an equation before using the Subtraction or Addition Properties of Equality. You should always simplify as much as possible before you try to isolate the variable. Remember that to simplify an expression means to do all the operations in the expression. Simplify one side of the equation at a time. Note that simplification is different from the process used to solve an equation in which we apply an operation to both sides.
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In the envelope model, what does an envelope represent?
- The equal sign
- The solution
- The variable
- A number one
Reveal answer
Answer: The variable
Source evidence
PDF page 213: We are going to use a model to clarify the process of solving an equation. An envelope represents the variable – since its contents are unknown – and each counter represents one. We will set out one envelope and some counters on our workspace, as shown in Figure 2.2. Both sides of the workspace have the same number of counters, but some counters are “hidden” in the envelope. Can you tell how many counters are in the envelope?
Elementary Algebra 2e
Elementary Algebra 2e by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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