Lesson 7 MA 152 Section 1.1 and 1.2 (part 1)Definitions:An equation is a statement indicating that two quantities are equal. Each unknown (represented by a letter) in an equation is a variable. A solution ( or root) of an equation is a value that makes a true statement when replaced for the variable. A solution set is the set of all solutions. To solve an equation is to find the solution(s).No value can be a solution of an equation that makes a denominator equal zero. Any equation that has a variable in a denominator may have restrictions on what value or values that may replace it. For example; in the equation 2242xx, x could not equal 2. The value 2 is restricted from possible values for x.More Definitions:Some equations are true no matter what value is replaced for the variable. Such an equation is called an identity. For example )2(22 xxxxis an identity. Some other equations, the variable may never be replaced by any value to make the equation true. This type of equation is called a contradiction. An example of a contradiction is the equation 522 xx. An equation that has a finite number of solutions is a conditional equation. An example of a conditional equation is 5324 xx (solution is -7).A linear equation is a first-degree polynomial equation and can be written in the form).0( 0 abaxEx 1: Solve each equation and categorize.) 5 3 2(3 4 )) 2( 1) 3( 2)6 18) 3( 3)2a x xb a a axc x+ = -+ = - --- =Ex 2: Solve each equation.1When the variables‘drop out’ on each side:false: no solutiontrue: infinite solutions3 7) 4 13 2) ( 2)( 3) ( 3)( 4)x xa xb x x x x+ ++ = +- - = + + rrrrrc2172)5()3()2(2 )2A rational equation is one that contains one or more rational expressions (fractions). Remember: no solutions can make zero denominators.Ex 3: Solve each.22 2 223 1 3) 2 22 3 3 2 5 2) 5 6 6 43 2) 12 4 4ax x xx x xbx x x x xa aca a a+ =- -+ - -+ =+ + + - -+- =+ + +A formula is an equation with more than one variable (sometimes several variables). Sometimes a formula may be written in as an equivalent in terms of a different variable. For example)32( toequivalent is 329559 FCCF. 3Ex 4: Solve each formula for the given variable.2) for ) ( ) for ha I prt rb A b B b== +In this lesson, we will cover the following types of application or applied problems that will be modeled with an equation.- Number problems- Geometric problemsThe textbook has a good strategy for solving application problems. I usually recommend the following 5-step strategy.1. Perhaps draw a picture or make a table after studying the problem. 2. Define the variable (state what x represents).3. Find a plan, formula, or sentence that will help you write an equation.4. Solve the equation.5. Answer the question asked in the problem.Solve each problem by writing an equation.1. Find three consecutive even integers so that the first added to twice the second is the same as twice the third.42. Marvin took 5 tests (each out of 100 points) during a semester. He made the samescore on the first test and the fifth test. Scores on the second, third, and fourth tests were 72, 85, and 79. If Marvin averaged 78, what was Marvin's score on the first test?3. A caterer charges $45 plus $8 per person. How many persons can Dawn have at her catered dinner, if she has budgeted no more than $140?54. Find the dimensions of a rectangle with a perimeter of 54 meters, if its length is 3 meters less than twice its
View Full Document
Unlocking...