Solve Linear Inequalities Quiz
The question sheet
Reveal any answer as you study-
What is a solution of an equation?
- The largest side of the equation
- Any number in the equation
- A value that makes a true statement
- A variable with no value
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 whether a number is a solution, what is Step 1?
- Substitute the number for the variable
- Simplify both sides first
- Check if the equation is true
- Isolate the variable
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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According to the Subtraction Property of Equality, if a = b, then:
- a ÷ c = b ÷ c
- a + c = b + c
- a − c = b − c
- a × c = 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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When you subtract the same quantity from both sides of an equation, you:
- reverse the sides
- lose the variable
- still have equality
- change the solution
Reveal answer
Answer: still have equality
Source evidence
PDF page 214: When you subtract the same quantity from both sides of an equation, you still have equality.
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To solve y + 37 = −13, which property is used?
- Commutative Property
- Addition Property of Equality
- Subtraction Property of Equality
- Distributive Property
Reveal answer
Answer: Subtraction Property of Equality
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 goal when solving these kinds of equations?
- Make both sides zero
- Add all the numbers
- Isolate the variable on one side
- Remove the equals sign
Reveal answer
Answer: 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 'undo' a subtraction from the variable, you should:
- divide both sides
- multiply both sides
- add the number to both sides
- subtract more from both sides
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 is the solution to a − 28 = −37?
- a = −9
- a = −65
- a = 9
- a = 65
Reveal answer
Answer: a = −9
Source evidence
PDF page 215: The solution to a − 28 = −37 is a = −9.
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Before isolating the variable, you should always:
- substitute a value
- check the answer
- simplify as much as possible
- divide both sides
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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To simplify an expression means to:
- apply operations to both sides
- isolate the variable
- substitute the solution
- do all operations in the expression
Reveal answer
Answer: do all operations in the expression
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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What is the solution to 5(n − 4) − 4n = −8?
- n = −8
- n = −4
- n = 8
- n = 12
Reveal answer
Answer: n = 12
Source evidence
PDF page 217: The solution to 5(n − 4) − 4n = −8 is n = 12.
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What is the first step in translating an English sentence to an equation?
- Solve the equation
- Translate the right words
- Locate the 'equals' word(s)
- Translate the left words
Reveal answer
Answer: Locate the 'equals' word(s)
Source evidence
PDF page 219: Step 1. Locate the “equals” word(s). Translate to an equals sign (=). Step 2. Translate the words to the left of the “equals” word(s) into an algebraic expression. Step 3. Translate the words to the right of the “equals” word(s) into an algebraic expression.
Elementary Algebra 2e
Elementary Algebra 2e by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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