Solving Linear Equations Define and use: Linear Equation in one variable, Solution types, Equivalent...
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Transcript of Solving Linear Equations Define and use: Linear Equation in one variable, Solution types, Equivalent...
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Solving Linear Equations
Define and use: Linear Equation in one variable,
Solution types,
Equivalent Equations
![Page 2: Solving Linear Equations Define and use: Linear Equation in one variable, Solution types, Equivalent Equations.](https://reader035.fdocuments.net/reader035/viewer/2022073121/5697c0101a28abf838ccb324/html5/thumbnails/2.jpg)
Linear Equations
You can use a variable (unknown value) to represent a quantity.
A solution is a set of values that make an equation true.
To solve an equation that has more than one operation, use the properties of equality to isolate the variable.
![Page 3: Solving Linear Equations Define and use: Linear Equation in one variable, Solution types, Equivalent Equations.](https://reader035.fdocuments.net/reader035/viewer/2022073121/5697c0101a28abf838ccb324/html5/thumbnails/3.jpg)
Use the properties of equality to solve the equation. (Let a, b, c = real numbers.)
Addition Property of Equality
Multiplication Property of Equality
If a=b, then a+c = b+c
If a=b, then ac = bc
Subtraction Property of Equality
Division Property of Equality
If a=b, then a-c = b-c If a=b, then a/c = b/c (c
![Page 4: Solving Linear Equations Define and use: Linear Equation in one variable, Solution types, Equivalent Equations.](https://reader035.fdocuments.net/reader035/viewer/2022073121/5697c0101a28abf838ccb324/html5/thumbnails/4.jpg)
Solve a Multi-Step Equation.
Solve 4(x-3) = -56. Show each step, and check the answer.
4(x-3) = -56 Given 4x –12 = -56 Distributive Property
4x-12+12 = -56 + 12 Addition Property = Division Property
x = -11 Simplify.
![Page 5: Solving Linear Equations Define and use: Linear Equation in one variable, Solution types, Equivalent Equations.](https://reader035.fdocuments.net/reader035/viewer/2022073121/5697c0101a28abf838ccb324/html5/thumbnails/5.jpg)
To Check your answer, substitute the solution into the equation
4(x-3) = -56 Given4(-11-3) = -56 Substitution4(-14) = -56 Simplify.-56 = -56 Verify.
![Page 6: Solving Linear Equations Define and use: Linear Equation in one variable, Solution types, Equivalent Equations.](https://reader035.fdocuments.net/reader035/viewer/2022073121/5697c0101a28abf838ccb324/html5/thumbnails/6.jpg)
Think and Discuss with your elbow partner.
1. What property is used to solve the equation x+3 = 9 ?
2. What property is used to solve the equation 12y = 36?
3. Explain how to solve the equation 4z-5 = 23.