Equations and Their Solutions

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Equations and Their Solutions

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Presentation transcript:

Equations and Their Solutions

Solutions of Equations Definitions: Equation – Is a mathematical statement that states that two expressions and or/quantities are equal. Examples: 4 + 6 = 10 3x = 15 11 = x - 4 Solution of an Equation – Is the value or values that make an equation true. Example: In the equation x + 4 = 7, “3” is the solution because it makes the equation true.

Solutions of Equations Determining Whether the Given Values Are Solutions to the Equations Example 1 a + 23 = 45 when a = 22 Example 2 60 ÷ c = 6 when c = 5 a + 23 = 45 22 + 23 = 45 ? 45 = 45 Original equation 60 ÷ c = 6 60 ÷ 5 = 6 ? 12 ≠ 6 Original equation Substitute the value given for the variable. Substitute the value given for the variable. Determine whether the two sides of the equation are equal. Determine whether the two sides of the equation are equal. 22 is a solution to this equation because 45 equals 45 5 is a not solution to this equation because 12 does not equal 6.

Solutions of Equations Determine whether the given values are solutions to the equations. 1.) 3x = 33 when x = 11 2.) z – 14 = 23 when z = 36 3.) 34 = 17b when b = 2 4.) 56 ÷w = 7 when w = 4

Solutions of Equations Real-Life Application Rachel is setting up for a party. She has a total of 5 centerpieces but needs a total of 14. Write an equation to determine how many more centerpieces that she needs to buy? If Rachel goes to the store to buy more centerpieces but they only have 7 available, will she have enough for the party?