Chapter 3 and Lessons 10

Solving Linear Equations with X²

Chapter 3 and Lessons 10.4, 10.5, 6.1 and 6.2

If the directions state:

“Solve for x…..or What is the solution set……or What are the roots……”and the problem has both an x²and an x, you make the equation equal to 0 and solve for x by factoring.

If the directions state:

“Solve for x……” and there is either an x²or an x, you solve to get x alone.

EXAMPLE 1:

6 = 3 – x

- 3 = - 3

3 = - x

-3 = x

- Original problem.

- To get x alone, subtract 3 from both sides.

- Since you CAN NOT have a negative x, you need to flip both to their opposite signs by multiply each side by -1.

Note the difference between the two examples (#1 above and #2 below). Example #2 is already set to equal 0 and example #1 isn't--

This is why they are solved differently.

Changing signs of equations:

If your answer turns out to have a negative x, you need to “flip” the x to positive and the number to its opposite. For example: if your answer was
–x = 2; you need to change it to x = -2 (by “flipping” each side to its opposite or by multiplying or dividing both sides by –1: flipping or multiplying or dividing will all give you the same results.)

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