Section P.7

 An expression is an algebraic statement that does not have an “=“  An equation is two expressions joined by an “=“

 A linear equation (in x) is one that can be written in the form ℝ

 The following all mean basically the same: ◦ Solve for x ◦ Find the solutions ◦ Find the roots ◦ Find the zeros

1. Simplify the algebraic expression on each side. 2. Collect the variable terms on one side and the constant times on the other side. 3. Isolate the variable. 4. Check your answer.

 Multiply both sides by the least common denominator (LCD)  Then solve as before

 Has the variable in a denominator  Must check for domain restrictions  Then solve as before ◦ Multiply by LCD to clear denominators

 Simplify and state the domain restrictions

 Read Section P.7  Page 81 #1-101 Every Other Odd, 108  Show work, or you will not receive credit

 In Exercises 1-16, solve and check each linear equation.  Exercises contain equations with constants in denominators. Solve each equation.

 Find the roots of

 A conditional equation has a limited number of real solutions, but at least one ◦ If you can solve and get x = #, and # is not a domain restriction  An inconsistent equation has no real solutions ◦ All x’s are eliminated and left with a false statement such as “7=0”  An identity has an infinite number of solutions, often all real numbers ◦ All x’s are eliminated and left with a true statement such as “3=3”

 Solve for r

 Solve S = P + Prt for t

 Find the roots of

 The absolute value of a number is its distance from zero.  |x| = a means x = a or x = -a  Solving an absolute value equation: 1. Isolate the absolute value. 2. If the absolute value equals a negative, there are no solutions. Otherwise, split the equation into two equations: one equal to positive, one equal to negative. 3. Solve each equation for x.

 Read Section P.7  Page 81 #1-101 Every Other Odd, 108  Show work, or you will not receive credit

 In Exercises 1-16, solve and check each linear equation.  Exercises contain equations with constants in denominators. Solve each equation.

 In exercises 51-58, determine whether each equation is an identity, a conditional equation, or an inconsistent equation.  In Exercises 59-70, solve each equation or state that it is true for all real numbers or no real numbers.  In Exercises 71-90, solve each formula for the specified variable.

 In exercises 51-58, determine whether each equation is an identity, a conditional equation, or an inconsistent equation.  In Exercises 59-70, solve each equation or state that it is true for all real numbers or no real numbers.  In Exercises 71-90, solve each formula for the specified variable.