8: Solving Linear Equations
- Page ID
- 114952
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Teetering high above the floor, this amazing mobile remains aloft thanks to its carefully balanced mass. Any shift in either direction could cause the mobile to become lopsided, or even crash downward. In this chapter, we will solve equations by keeping quantities on both sides of an equal sign in perfect balance.
- 8.2: Solve Equations Using the Subtraction and Addition Properties of Equality
- The purpose in solving an equation is to find the value or values of the variable that make each side of the equation the same. Any value of the variable that makes the equation true is called a solution to the equation. We can use the Subtraction and Addition Properties of Equality to solve equations by isolating the variable on one side of the equation. Usually, we will need to simplify one or both sides of an equation before using the Subtraction or Addition Properties of Equality.
- 8.3: Solve Equations Using the Division and Multiplication Properties of Equality
- We can also use the Division and Multiplication Properties of Equality to solve equations by isolating the variable on one side of the equation. The goal of using the Division and Multiplication Properties of Equality is to "undo" the operation on the variable. Usually, we will need to simplify one or both sides of an equation before using the Division or Multiplication Properties of Equality.
- 8.4: Solve Equations with Variables and Constants on Both Sides)
- You may have noticed that in all the equations we have solved so far, all the variable terms were on only one side of the equation with the constants on the other side. This does not happen all the time—so now we’ll see how to solve equations where the variable terms and/or constant terms are on both sides of the equation.
- 8.5: Solve Equations with Fraction or Decimal Coefficients
- The General Strategy for Solving Linear Equations can be used to solve for equations with fraction or decimal coefficients. Clearing the equation of fractions applies the Multiplication Property of Equality by multiplying both sides of the equation by the LCD of all fractions in the equation. The result of this operation will be a new equation, equivalent to the first, but with no fractions. When we have an equation with decimals, we can use the same process we used to clear fractions.
Figure 8.1 - A Calder mobile is balanced and has several elements on each side. (credit: paurian, Flickr)
Contributors and Attributions
Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/fd53eae1-fa2...49835c3c@5.191."