4.2+Solving+Linear+Equations+0809

Kwang Su L.
__ **Say it With Symbols** __ Big Idea Equations can be used to model real things. ** Essential Question # 4 - How do I create and solve equations? **
 * Problem 4.2 Solving Linear Equations**

Golden Rule of Algebra ~ What you do to one side you have to do to the other!
 * Notes**

The example below shows one way to solve the equation 100 + 4x = 25 + 7x

100 + 4x = 25 + 7x 100 + 4x - 4x = 25 + 7x - 4x 100 = 25 + 3x 100 - 25 = 25 + 3x - 25 75 = 3x 75/3 = 3x/3 25 = x


 * A. Supply an explanation for each numbered step in the above solution to 100 + 4x = 25 + 7x**

1. We need to isolate one side so we decided to isolate 100 to get rid of 4x, so we - 4x to get 100 isolated and we did that to the other side of the equation (7x - 4x) to get 100 = 25 + 3x

2. Next we want to get rid of 25,, so we minus 25 from both sides to get 75 = 3x

3. Now we just have to get x isolated by dividing 3x / 3x = x and then we do that to the other side, 75 / 3 = 25. So x = 25


 * B. Show a solution with a different step**

100 + 4x = 25 + 7x 4x - 7x = 25 -100 -3x = - 75 x = - 75 / - 3 x = 25

Here I put all x values on one side and non x values on the other side and then dived -3 / -3 to get x and do that to the other side to get x = 25

100 + 4(25) = 25 + 7(25) 100 + 100 = 25 + 175 200 = 200 This is correct I did this by substituting 25 for x
 * C. How can you check that x = 25 is the correct solution?**


 * Problem 4.2 Follow Up**


 * 1. Fill in the details that were omitted**

11x - 12 = 30 + 5x 11x = 42 + 5x 6x = 42 x = 7

a. You can isolate any side so let's decide to isolate 11x. To do that add 12 to -12, which makes it zero nad add 12 to 30 = 42. So the next equation is 11x = 42 + 5x

b. Now we want to isolate the5x so we subtract -5x to +5x = 0 and then subtract -5x from 11x which gives you 6x = 42

c. We want now x really isolated so we divide 6x /6x and we do that same on the other side and finally we x = 7

We substitute x for 7 in the equation 11(7) - 12 = 30 + 5(7) 77 - 12 = 30 + 35 65 = 65 This is correct since both the solutions came out equal
 * 2. How can you check that x = 7 is the correct solution?**

I would see the lines of the graph intersect each other to show equality and see the y values and spot the equal y values for both equations on the table.
 * 3. Explain how you could use a graph and table to solve the equation 11x - 12 = 30 + 5x**