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8th GRADE MATH NOTES—Chapter 1Section 1.1/1.2—Equation Points to Remember Try to isolate the variable (get it by itself). To do this, perform the inverse (think opposite) operation of what is listed adjacent to the variable.Whatever you do to one side, also do the same thing to the other side of the equation.In a two-step equation, try to isolate the variable term first. Then on the next step, isolate the variable itself.(Example: In 3x + 5 = 26, first isolate the 3x by subtracting 5 from each side. Then isolate x by dividing each side by 3)3x + 5 = 26 -5 - 53x = 21---- ---- 3 3x = 7An equation may have no solution, one solution, more than one solution, or infinite solutions.X – 3 = x + 5 (no solution)X + 5 = 7 (one solution)X + 4 = 4 + x (infinite solutions)Always substitute your solution in for x to check your solution. Example x + 9 = 10 1 + 9 = 10 -9 -9 10 = 10X = 1 TrueSECTION 1.3—EquationsIn an equation with the same variable on both sides (Ex. 4x – 5 = 2x + 5), get all of the variables on the same side and then solve as a 2 step equation. In the example, subtract 2x from both sides to keep the equation balanced.4x – 5 = 2x + 54x – 2x – 5 = 2x – 2x + 52x – 5 = 52x – 5 + 5 = 5 + 52x = 10x = 5 If you are correctly working with an equation and end up with a false statement, the equation has no solution. If you are correctly working with an equation and end up with a TRUE statement, the equation has infinite solutions.NOTES 1.4—Literal Equations To rewrite a literal equation, solve for one variable in terms of the other variable or variables. Using inverse operations, work the equation the same way you would with numbers.Example: Solve y = mx + b for m y – b = mxSubtraction of both sides (y – b) = mDivide both sides by x--------- x ................
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