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Questions and Answers
Over this unit, we will learn about linear expressions, which are _____________ _________________________________________________________________.
Over this unit, we will learn about linear expressions, which are _____________ _________________________________________________________________.
mathematical phrases that contain numbers, variables, and operators
The difference between a linear expression and a Linear Equation is that ______ ________________________________________________________________.
The difference between a linear expression and a Linear Equation is that ______ ________________________________________________________________.
a linear equation contains an equals sign
This scale represents an _________ _______ because the equation ___________________________________ in order to be correct.
This scale represents an _________ _______ because the equation ___________________________________ in order to be correct.
equal balance; must maintain the same value on both sides
Any time we are asked to 'solve', 'evaluate', 'find', or 'identify', we are simply being asked to determine what the _______ is for that specific question.
Any time we are asked to 'solve', 'evaluate', 'find', or 'identify', we are simply being asked to determine what the _______ is for that specific question.
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Last unit, we would create a Table of Values for a specific expression, say 6+h. We would input a new _____________ for each variable and the output was our answer.
Last unit, we would create a Table of Values for a specific expression, say 6+h. We would input a new _____________ for each variable and the output was our answer.
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By Inspection, we can use mental math to find the value of the variable. For example, we can ask, 'What number added to 6 gives us 11?'. We can also say ___________________________________________________.
By Inspection, we can use mental math to find the value of the variable. For example, we can ask, 'What number added to 6 gives us 11?'. We can also say ___________________________________________________.
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We can use manipulatives or draw either Cups & Counters or _______ _______ to solve an equation.
We can use manipulatives or draw either Cups & Counters or _______ _______ to solve an equation.
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We will need to work backwards. We will be given a full equation with a variable, like 6+h=11, and need to figure out how to find the _______ of h for this example.
We will need to work backwards. We will be given a full equation with a variable, like 6+h=11, and need to figure out how to find the _______ of h for this example.
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An opposite operation ________________________________________.
An opposite operation ________________________________________.
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When we are working with _____________ numbers, the opposite operation is our best bet.
When we are working with _____________ numbers, the opposite operation is our best bet.
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That means __________________________________________ ____________________________________________________________.
That means __________________________________________ ____________________________________________________________.
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That is why this method is also sometimes called 'isolating the variable.'
That is why this method is also sometimes called 'isolating the variable.'
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When you find your answer, substitute it into your original question. If the statement is accurate, you know that you got the right __________.
When you find your answer, substitute it into your original question. If the statement is accurate, you know that you got the right __________.
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A number that is directly beside a variable (also called a _____________ _____________) means that we multiply.
A number that is directly beside a variable (also called a _____________ _____________) means that we multiply.
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We can also use a division sign so that the phrase, 'a number divided by 5 equals 8,' could be written as ______________.
We can also use a division sign so that the phrase, 'a number divided by 5 equals 8,' could be written as ______________.
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When we are solving algebraic equations, however, we work ______________.
When we are solving algebraic equations, however, we work ______________.
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Step 1: Rewrite the problem, Step 2: Remove the _____________.
Step 1: Rewrite the problem, Step 2: Remove the _____________.
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Step 3: Remove the numerical _____________.
Step 3: Remove the numerical _____________.
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Study Notes
Solving One-Step Linear Equations
- Linear expressions are mathematical phrases containing variables, numbers, and operations.
- A linear equation is a statement that two linear expressions are equal.
- The key parts of an expression are variables, numbers, and operations.
- "Preservation of equality" refers to keeping both sides of an equation equal throughout the solution process. This is done by performing the same operation on both sides.
- Solving a one-step equation means finding the value of the variable in the equation. This is similar to finding the output in a function. The difference is when given an equation we now have to work backwards.
Modeling Equations
- Cups & Counters, Algebra Tiles, and Equal Expressions are methods for visually representing equations.
- A scale used in modeling represents equality, and balancing ensures both sides are equal.
Strategies for Solving One-Step Equations
- By Inspection: Use mental math to find the variable's value. For example, to solve 6 + h = 11, find the number that added to 6 equals 11.
- By Modeling: Use visuals (like Cups & Counters or Algebra Tiles) to represent and solve the equation. This method is helpful for visual learners but can be time-consuming.
- By Using the Opposite Operation: Isolate the variable by applying the inverse operation to both sides of the equation. For example, if 6 is added to the variable you subtract 6 from both sides to isolate the variable.
One-Step Equations with Multiplication and Division
- A numerical coefficient (number directly next to a variable) represents multiplication.
- Division can be represented using a division symbol (÷) or a fraction.
- The methods for solving one-step equations (by inspection, modeling, and opposite operations) also apply to multiplication and division equations.
Solving Two-Step Equations
- A two-step equation requires more than one operation to isolate the variable.
- Don’t try to solve all steps at once or make all calculations in your head. Show all your work!
- To solve two-step problems like 3x + 4 =19: First, rewrite the problem, then remove the constant, remove the numerical coefficient to isolate the variable, then square your answer.
- Algebra tiles or visuals can also solve two-step equations.
- To solve a two-step equation, it’s important to follow the order of operations in reverse (often using the acronym BEDMAS).
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Description
This quiz focuses on solving one-step linear equations and understanding key concepts such as linear expressions and the preservation of equality. It includes modeling equations using visual methods and strategies for finding variable values. Test your knowledge and improve your algebra skills!
