Solutions of a linear equation
- 2. • Help Session – Link • IXL – Housekeeping
- 3. • Students transform equations into simpler forms using the distributive property. • Students learn that not every linear equation has a solution. Unit 2: Lesson 6 Solutions of a Linear Equation
- 4. Solve the linear equation 1 5 x + 13 + x = 1 − 9x + 22
- 5. The distributive property can be used to both expand and simplify expressions. We have already used the distributive property to “collect like terms.” For example, 2x + 6x = (2 + 6)x = 8x. We have also used the distributive property to expand expressions. For example, 2(x + 5) = 2x + 10. The Distributive Property
- 6. In this lesson, we will continue to use the distributive property to solve more complicated equations. Also highlighted in this lesson is a common error that is made when using the distributive property, which is multiplying a factor to terms that are not part of the group. For example, in the expression 3(x + 1) − 5, students should know that they do not distribute the factor 3 to the term −5 because it is not in the group (x + 1).
- 7. What value of x would make the linear equation 4x + 3(4x + 7) = 4(7x + 3) − 3 true? What is the “best” first step and why? Example 1
- 8. What value of x would make the following linear equation true: 20 − (3x − 9) − 2 = −(−11x + 1)? Example 2
- 9. What value of x would make the following linear equation true: 1 2 (4x + 6) − 2 = −(5x + 9)? Example 3
- 10. Consider the following equation: 2(x + 1) = 2x − 3. What value of x makes the equation true? Example 4
- 11. Can you think of a value of x that would make this equation true? 2(x + 1) = 2x − 3 Why do you think this happened? We know that an equation is a statement of equality. The linear expressions were such that they could not be equal to each other, no matter what value was substituted for x. What can we conclude?
- 12. What value of x would make the following linear equation true: 9(4 − 2x) − 3 = 4 − 6(3x − 5)? Try this one!
- 13. Can you think of an equation that has no solution??? Think of your own!
- 14. Find the value of 𝒙𝒙 that makes the equation true. 1. 17 − 5(2x − 9) = −(−6x + 10) + 4 2. −(x − 7) + 5 3 = 2(x + 9) 3. 4 9 + 4(x − 1) = 28 9 − (x − 7x) + 1 4. 5(3x + 4) − 2x = 7x − 3(−2x + 11) 5. 7x − (3x + 5) − 8 = 1 2 (8x + 20) − 7x + 5 6. Write three equations that have no solution Practice
- 15. The distributive property is used to expand expressions. For example, the expression 2(3x − 10) is rewritten as 6x − 10 after the distributive property is applied. The distributive property is used to simplify expressions. For example, the expression 7x + 11x is rewritten as (7 + 11)x and 18x after the distributive property is applied. The distributive property is applied only to terms within a group: 4(3x + 5) − 2 = 12x + 20 − 2. Notice that the term -2 is not part of the group and, therefore, not multiplied by 4. When an equation is transformed into an untrue sentence, such as 5 ≠ 11, we say the equation has no solution. Summary
- 16. Wrap Up • We know how to transform equations into simpler forms using the distributive property. • We now know that there are some equations that do not have solutions. What now??? • IXL Skill U.7 – Solve Multi-Step Equations • IXL Skill U.8 – Solve Equations Involving Like Terms • IXL Skill U.9 – Solve Equations With Variables on Both Sides • IXL Skill U.10 – Solve Equations: Mixed Review