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Math A Review

Equations and Word Problems

Solving Equations
1)    Multiply through any factors                        ex.    9 + 2(5x + 3) = 13x            check
2)    Combine like terms on the same side.                9 + 10x +6 = 13x               9 + 2(5(5) + 3) = 13(5)
3)    Combine like terms on opposite sides.                  15 + 10x = 13x                9 + 2(28) = 65
4)    Solve equation.                                                          - 10x    -10x                  9 + 56 = 65
5)    Check                                                                            15 = 3x                        65 = 65 checks
                                                                                                5=x

Solving Inequality Equations
--Solve as you would normally and keep inequality sign with one exception, Dividing or multiplying by a negative number changes the inequality sign to it's opposite.
 
Word Problems
Read all word problems carefully.  It is easy to make a mistake in the let statement.
1.    Make a "let statement."
2.    Translate the words of the problem into algebraic phrases.
3.    Solve for the variable.
4.    Substitute the value of the variable in the "let" statement to find the other answers
       (when necessary)
5.    Check your answer in the WORDS of the problem.

Special Number Problems:  sample let statements
    Consecutive Integers:    Differ by 1    ex.    let x = 1st integer, x+1 = 2nd integer,
                                                                     x+2 = 3rd integer
    Odd or Even Consecutive Integers:    Differ by 2    ex.    Let x = 1st integer, x+2 = 2nd integer,
                                                                                          x+4 = 3rd integer