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Variables and Equations

Variables and Equations. Pre-Algebra. Learning Objective. I can solve equations with variables. Vocabulary. Equation A mathematical sentence formed by placing an equal sign between two expressions. Example: x - 8 = 12 Solution

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Variables and Equations

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  1. Variables and Equations Pre-Algebra

  2. Learning Objective • I can solve equations with variables.

  3. Vocabulary • Equation • A mathematical sentence formed by placing an equal sign between two expressions. • Example: x - 8 = 12 • Solution • A number that produces a true statement when substituted for the variable in an equation. • Example: 2 + x = 5; x=3 is a solution

  4. Example 1 - Writing Verbal Sentences as Equations • The sum of x and 6 is 9. • Equation: x + 6 = 9 • The difference of 12 and y is 15. • Equation: 12 - y = 15 • The product of -4 and p is 32. • Equation: -4p = 32 • The quotient of n and 2 is 9. • Equation: n/2 = 9

  5. Example 2: Checking Possible Solutions • Tell whether 9 or 7 is a solution of x - 5=2. • Substitute 9 for x • x - 5 = 2 • 9 - 5 = 2 ? • 4  2 • 9 is not a solution

  6. Example 2: Checking Possible Solutions • Tell whether 9 or 7 is a solution of x - 5=2. • Substitute 7 for x. • x - 5 = 2 • 7 - 5 = 2 ? • 2 = 2  • 7 is a solution

  7. Skill Check • Write the verbal sentence as an equation. • The sum of 3 and z is -10. • 3 + z = -10 • The quotient of m and 6 is 4. • m/6 = 6 • Tell whether -5 or 5 is a solution of -8y=40. • -5 is a solution

  8. Example 3 - Solving Equations Using Mental Math • Equation: x + 3 = 11 • Question: What number plus 3 equals 11? • Solution: 8 • Check: 8 + 3 = 11  • Equation: 16 - m = 9 • Question: 16 minus what number equals 9? • Solution: 7 • Check: 16 - 7 = 9 

  9. Example 3 - Solving Equations Using Mental Math • Equation: 20 = 5t • Question: 20 equals 5 times what number? • Solution: 4 • Check: 20 = 5(4)  • Equation: y/6 = -3 • Question: What number divided by 6 equals -3? • Solution: -18 • Check: -18/6 = -3

  10. Skill Check • Solve the equations using mental math. • x - 10 = 7 • x = 17 • 2 + n = -6 • x = -8 • 3w = -15 • x = -5 • 4 = 36/x • x = 9

  11. Skill Check • Go-cart rides cost $5 each at a county fair. During the first day of the fair, the go-cart operator takes in a total of $1000. How many times did people ride the go-carts that day? Write and solve an equation to find the answer. • 5x = 1000, x = 200; 200 times

  12. Classwork Assignment • Page 87-88 #s 8-15, 20-31 even, 32-34

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