How to Understand Textbook Algebra
Textbook algebra teaches you how to work with variables. Algebra is essential for many careers such as architecture, engineering, nursing and accounting. Textbook algebra covers polynomials, graphing, exponents, inequalities and using equations to solve for variables. Understanding algebra takes practice. Textbook algebra takes you step by step to help you build a strong foundation in algebra. Algebra is required for any higher level math courses and makes understanding other mathematics much easier.
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Instructions
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Learn how to solve a basic equation, or linear equation, for a single missing variable. This is the basis for understanding Algebra.
For example, solve for x in the equation x + 5 = 9.
Isolate x by subtracting 5 from each side of the equation. Anything you do on one side of the equation, you must do on the other in order to balance the equation.
The equation now looks like this: x + 5 -- 5 = 9 -- 5.When x is completely isolated, you have your solution. The final answer becomes x = 4.
In order to cancel out numbers, perform the opposite operation. For instance, to cancel out multiplication, divide and vice versa.
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Learn how to solve equations with two variables. These are typically in pairs called systems of equations. You can substitute one equation into another.
For example, solve for x and y in the equations x + 5y = 2 and x + y = 6.
Isolate x in one of the equations first. In the equation x + 5y = 2, subtract 5y from both sides. This leaves you with x = 2 -- 5y.Substitute the x value into the second equation. The second equation now looks like 2 -- 5y + y = 6. Simplify the expression. This means combine all like terms. The equation now looks like 2 -- 6y = 6. Solve for y.
Subtract 2 from both sides and divide by -6. 2 -- 2 -- 6y = 6 -- 2. -6y = 6. -6y/-6 = 4/-6. The final answer for y is -4/6. However, all fractions should be simplified. Since 2 goes into both the numerator and denominator, the final fraction is -2/3.
Place the y value into the equation where you isolated x. x = 2 -- 5(-2/3). Solve for x.
x = 2 -- (-10/3) Two negatives become a positive.x = 2 + 10/3 Find a common denominator and add the two fractions.
x = 6/3 + 10/3
x = 16/3 -
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Understand how to graph x and y solutions. The x value is the horizontal axis. The y value is the vertical axis. Always locate the x coordinate first and then move up or down to the y coordinate.
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Practice all problems associated with each lesson. This will help you understand the basic skills necessary to be successful with algebra.
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Memorize all formulas or create an index card with important formulas such as slope and the quadratic equation.
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Work through each lesson completely before moving on to the next. Each lesson builds upon the others.
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Tips & Warnings
Once you know how to solve for missing variables, algebra becomes easier to understand. Missing variables can be any letter of the alphabet, but are typically x, y and z.
Never accept a solution without testing it. Test all solutions by placing the solved values back into the equation. This will ensure your answer is correct.
