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Mastering Multi-Step Equations: Isolating Variables and Using Inverses

In this section, we explore the process of solving multi-step equations to isolate variables and find their values. Understanding properties of equality is crucial: when you add or multiply one side, you must do the same to the other. We’ll practice using additive and multiplicative inverses, like finding the additive inverse of -10 (which is 10) and confirming our solutions. Additionally, we discuss combining like terms and using grouping symbols. Complete the assignments to reinforce your understanding!

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Mastering Multi-Step Equations: Isolating Variables and Using Inverses

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  1. Chapter 2: Section 2 Solving multi-step equations

  2. Remember our goal… • When we solve equations we want to isolate the variable to discover its value. • We want to find out how much the variable equals. • Solution of the Equation: the value of the variable that makes the equation true

  3. Also, remember our properties of equality… • Addition • What you add to one side, you must aslo…? • Multiplication • If you multiply one side of the equation by a number, you must…?

  4. What happens if there is multiplication and addition? Work backwards- the opposite direction of the order of operations. What’s the additive inverse of -10? 10 Additive identity! Now, we should multiply both sides by which number? In other words: what is the multiplicative inverse of 2? Now check your work and see if it checks out!!!

  5. How ‘bout another example? What is the additive inverse of -6? 6 We get the additive identity! Multiply both sides by 9, why? Now check your work and see if it checks out!!!

  6. Now you try

  7. Assignment • Page 84 • Numbers 2-38 even • And number 58

  8. Chapter 2: Section 3 Solving multi-step equations with grouping symbols

  9. Remember our goal… • When we solve equations we want to isolate the variable to discover its value. • We want to find out how much the variable equals. • Solution of the Equation: the value of the variable that makes the equation true

  10. Also, remember our properties of equality… • Addition • What you add to one side, you must aslo…? • Multiplication • If you multiply one side of the equation by a number, you must…?

  11. What if we need to combine like terms? Work backwards- the opposite direction of the order of operations. Just combine your like terms! Use your additive inverse as you work backwards. Now, we should multiply both sides by which number? In other words: what is the multiplicative inverse of 3? Now check your work and see if it checks out!!!

  12. Try these please

  13. What about grouping symbols? Distribute to get rid of parentheses. Just combine your like terms! Use your additive inverse as you work backwards. Now, we should multiply both sides by which number? In other words: what is the multiplicative inverse of 3? Now check your work and see if it checks out!!!

  14. Try these please

  15. Assignment • Page 91 • Numbers 2-28 even • And also 53 and 65

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