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This chapter is divided into three parts:
I. Simple Equations
II. Complex Expressions with Exponents
III. Manipulating Complex Expressions
IV. Inequalities
I. Simple Equations
A. Fundamental Definitions
B. Single-Variable Equations
C. Solving Two Variables
D. More than Two Variables
E. Solving for Expressions
F. Equation Trick Questions
A. Fundamental Definitions
Variable |
Algebra is all about variables. These are unknown quantities that are usually expressed as a letter such as x or y. |
Coefficient |
This is a number next to a variable that describes how many of the variable there are. For example, 4x, where 4 is the coefficient. |
Constant |
These are fixed numbers. 4x + 7, where 7 is the constant. |
Equation |
This is where at least two expressions separated by an equal sign, eg. 4x = 4y + 2. |
Solution/Root |
What values for the variables will solve the equation? |
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NOTE: Shortcuts in Algebra
Keep in mind that the GMAT is NOT a standard achievement test. The test measures your resourcefulness and intellect in solving problems, not the methods achieved to do so. This means that you should use shortcuts whenever you can.
This means that you should freely use ALL THE ADVANCED TECHNIQUES, such as Plug in, Backsolving and Experiments (see math introductory chapter). Some GMAT questions are designed to be solved this way.... and doing the conventional algebra will take too much time. Don't be afraid to start Backsolving or Plugging in as soon as you hit a brick wall.
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B. Solving Single Variable Equations (Beginner)
You goal in algebra is usually to take complex equations and reduce them to something resembling a single variable equals a constant, such as x = 4.
But getting to that point on the GMAT will rarely be easy! You'll have to add, subtract, divide, multiply, square (or even cube) both sides of an equation. View equations as a balancing act. As long as you do something to both sides, you are all set.
2x + 7 = 19 |
Subtract 7 from both sides |
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2x = 12 |
Divide both sides by 2 |
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x = 6 |
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√x + 1 = 10 |
Subtract 1 from both sides |
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√x = 9 |
Square both sides |
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x = 81 |
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In addition to manipulating both sides of the equation, you'll have to Distribute and Combine Like Terms to help you get to the simple final expression of "x = ?".
| Distribute |
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a(b + c) = |
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(a × b) + (a × c) = |
Distribute the a value by multiplying b and c. |
Combining Like Terms |
2x + 3x + 7 = 15 |
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5x + 7 = 15 |
Combine the x's.
Note: When you combine terms they must have the same exponent and variable. |
This is a partial free sample of our prep guide. To view the remainder of this page, purchase the 800score.com Prep Course.
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