Download MAT 1033 – Intermediate Algebra Equation Solving Review

MAT 1033 – Intermediate Algebra
Equation Solving Review
Solving Linear Equations of One variable
Ax  B  C
1.
2.
3.
4.
5.
6.
7.
Identify that it is a linear equation of one variable. Visually, one variable should be present and
there should be no exponents (other than a 1) on the variable.
Clear any decimals by multiplying by the appropriate power of 10 and clear fractions by
multiplying every term on both sides by the LCD.
Use the distributive property to remove any parentheses.
Collect like terms on each side of the equal sign.
Using the addition property of equality get all terms with the variable on one side and every term
without a variable on the other side of the equation.
Collect like terms and divide by the coefficient on the variable.
Check your solution in the original equation!
Note: It is possible to get No Solution or an Infinite Amount of Solutions.
See Problems 13,15 on MAT 1033 Final Exam Review
Solving Rational Equations
1. Identify that is a rational equation by looking for rational expressions. A good clue is that there
are variables in at least one denominator.
2. Factor the denominators if possible.
3. Determine what numbers the variable cannot be based on the denominators.
4. Determine the least common denominator (LCD).
5. Multiply each side of the equation by the LCD.
6. Use the distributive law so that each term is multiplied by the LCD.
7. Divide out the common factors.
8. Solve the resulting equation.
9. Check your solutions in the original rational equation! If any of these possible solutions
correspond to the numbers from step 3 thus make a denominator zero, then they are NOT
solutions to the original equation and must be rejected.
See Problems 14,18,19 on MAT 1033 Final Exam Review
Solving Literal Equations or Formulas for a Specified Variable
1. If the equation or formula has fractions then multiply both sides by the LCD to clear the fractions.
2. Using the addition property of equality, get all the terms with the specified variable on one side
and every term without the specified variable on the other side of the equation.
3. If the specified variable is in more than one term then factor it from each term.
4. Divide each side by the factor that is the coefficient of the specified variable.
See Problems 35,36,37,38 on MAT 1033 Final Exam Review
MAT 1033 – Intermediate Algebra
Equation Solving Review
Solving Absolute Value Equations
Ax  B  C
1. Identify that is an absolute value equation. You will see an absolute value symbol in the
equation.
2. Isolate the absolute value expression on one side of the equation.
3. Rewrite the absolute value equation into two associated linear equations.
Ax  B  C
or Ax  B  C
4. Solve these two equations for the variable.
5. Check your solution(s) in the original absolute value equation!
See Problem 22 on MAT 1033 Final Exam Review
Solving Quadratic Equations
ax2  bx  c  0
1. Identify that the equation is quadratic. The highest exponent on a variable should be 2.
2. Write in standard form: ax 2  bx  c  0 (except for the square root property).
3. At this point, there are several approaches to solving the equation.
a. Factoring-Use zero factor property: If ab = 0, then a = 0 or b = 0.
i)
Factor completely.
ii)
Set each factor equal to zero and solve for the variable to find solutions.
iii)
Check the values in the original equation.
b. Square Root Property- If x 2  b , then x  b or x  b .
i)
Isolate term with the variable that is squared on one side of the equation.
ii)
Use the square root property to take the square root of each side of the
equation.
iii)
Solve for the variable and simplify the solutions.
c. Completing the Square
i)
Isolate the constant term on one side of the equation.
ii)
Divide every term by a.
iii)
Take ½ of the linear term’s coefficient and square it.
iv)
Add this number to both sides of the equation.
v)
Factor the trinomial into a square of a binomial.
vi)
Use the Square Root Property and solve for the variable.
vii)
Check the solutions in the original equation.
2
d. Quadratic Formula x  b  b  4ac
2a
i)
Evaluate the quadratic formula for the coefficients a, b, and c.
ii)
Check the solutions in the original equation.
4. Remember that solutions to quadratic equations can be non-real complex numbers (imaginary).
See Problems 16,17,20,21,23,24,25,26,27,28 on MAT 1033 Final Exam Review