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# 1 1 solving simple equations

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• 1. 1-step Equations: + and – 9/23/13 In elementary school, you solved equations that looked like this: In Algebra, we just use a variable instead of the box! We could rewrite the same equation like this: x + 3 = 5
• 2. To solve: Need to get x by itself. We must “undo” whatever has been done to the variable. Do the same to BOTH SIDES of the = sign! Answer should be: x = some number.
• 3. Equations Have to Balance! Both sides of the = sign must “weigh” the same! When you change one side, do the same to the other side, so it stays balanced! x + 3 = 7
• 4. Examples: Solve each equation. Check your answers! x + 3 = -7 m – 6 = 8
• 5. 3.4 + a = 0.5 y – 1.3 = -3.9
• 6. 1/4 = 1/2 + t -2/5 = x – 1/3
• 7. You Try! Solve each equation. Check your answers! x – 9 = -6 1.6 + n = 10.7
• 8. 1-step Equations: × and ÷ 9/24/13 Just like with adding and subtracting, we need to “undo” what is done to x. Use division to “undo” multiplication. Use multiplication to “undo” division. Remember: A fraction bar means divide! Example: says x divided by 3!
• 9. Examples: Solve each equation: 2x = 8 12.9 = -3.2b
• 10. You Try! Solve each 1-step equation. -4.2a = 16.6
• 11. Applications 9/26/13 How to solve a word problem using a linear equation: 1. Write a verbal model 2. Define a variable for the unknown 3. Write an equation 4. Solve 5. Answer the question in sentence form
• 12. Common Language: In a word problem: “is” means = “of” means multiply “per” means multiply “less than” usually means subtract “more than” usually means add
• 13. Example 1 Paula has 3 more dolls than her friend Briana. If Paula has 10 dolls, write and solve an equation to find out how many dolls Briana has. Let be Paula’s dolls Briana’s dolls + 3= Briana’s dollsb 10 = b + 3
• 14. You Try! A used book costs \$17 less than the same book new. The used book costs \$9. Write and solve an equation to find out how much the new book cost.
• 15. Example 2 The melting point of bromine is of the melting point of nitrogen. The melting point of bromine is −7 C. Write and solve an equation to ﬁnd the melting point of nitrogen. Let be the Melting point of bromine 1/30 Melting point of nitrogen = Melting point of nitrogenn -7 = 1/30 n
• 16. You Try! The melting point of mercury is about of the melting point of krypton. The melting point of mercury is −39 C. Write and solve an equation to ﬁnd the melting point of krypton.
• 17. Example 3 John earns \$5 per hour mowing lawns. Write and solve an equation to find how many hours he must work to earn \$40. Let be the Amount earned \$5 # of hours= # of hoursh 40 = 5 h
• 18. You Try! If you save at a rate of \$15 per month, how long will it take you to save \$135? Write and solve an equation.