1. © A Very Good Teacher 2007 Exit Level TAKS Preparation Unit Objective 4

2. © A Very Good Teacher 2007 Writing Equations and Inequalities 4, Ac3A Identify if the situation warrants an equation (=) or an inequality (, ≤, ≥). Equations are used when quantities are equal. Inequalities are used when quantities are not equal.  Look for words like: No more than No less than At least At most

3. © A Very Good Teacher 2007 Writing Equations and Inequalities, cont… Example: A used car salesman is paid a salary of $200 per week plus at least a 10% commission. If x represents the salesman’s total sales, which of the following could be used to determine y, the salesman’s weekly income? Equation or Inequality? The words “at least” indicate that this will be an inequality. 4, Ac3A Now write the inequality.y ?200+.10x Total incomeSalary + Commission Could be greater than or exactly ≥

4. © A Very Good Teacher 2007 Solving Equations and Inequalities Write the equation or inequality (if necessary) Substitute any given values Remember to use inverse operations to solve Example: Hanna makes necklaces that she sells at a local craft show. She pays $50 a day to rent the booth and each necklace costs $3.50 to make. If she sells each necklace for $9, how many necklaces does she need to sell to make a profit during a 3 day weekend at the craft show? 1. Write the equationProfit = 9x – (3.5x + 50(3)) 4, Ac3B

5. © A Very Good Teacher 2007 Solving Equations and Inequalities, cont… Now that we have an equation, we can substitute any given values We can replace ‘profit’ with zero to find the break even point Profit = 9x – (3.5x + 50(3)) 0 = 9x – (3.5x + 50(3)) Now Solve 0 = 9x – 3.5x - 50(3) 0 = 9x – 3.5x - 150 0 = 5.5x - 150 +150 150 = 5.5x 5.5 5.5 27.27 = x 4, Ac3B

6. © A Very Good Teacher 2007 Solving Equations and Inequalities, cont… The most important part of solving equations involving word problems is checking for reasonableness According to our equation x = 27.27 Can Hanna sell 27.27 necklaces? So the answer must be a whole number Is it 27? No, selling 27 necklaces would not make a profit The answer is 28 necklaces! 4, Ac3B

7. © A Very Good Teacher 2007 Writing Systems of Equations Most systems are comprised of 2 types of equations A total equation that represents the total number of items And a comparison equation that represents the relationship between the two variables Identify what the variables represent Identify which numbers go with each equation type. 4, Ac4A

8. © A Very Good Teacher 2007 Writing Systems of Equations, cont… Example: Claudia purchased 12 shirts and jeans for the school year. Jeans cost $22 and shirts cost $15. If Claudia spent a total of $215, write a system of equations that could be used to find the number of shirts that Claudia purchased. 4, Ac4A Total EquationComparison Equation j + s = 12 22j + 15s = 215

9. © A Very Good Teacher 2007 Solving Systems of Equations The solution to a system of linear equations is the point where the two lines intersect. If you are unsure how to solve a problem by substitution, elimination, or graphing, you can substitute each answer choice into the equations to see which one works for BOTH equations. 4, Ac4B

10. © A Very Good Teacher 2007 Solving Systems of Equations, cont… Example: The equations of two lines are 4x – y = 3 and y = 5x – 2. What is the value of x in the solution for this system of equations? 4, Ac4B A.x = -2 B.x = -1 C.x = 2 D.x = 1 4x – y = 3 y = 5x - 2 4(-2) – y = 3 -8 – y = 3 +8 +8 – y = 11 y = -11 y = 5(-2) - 2 y = -10 - 2 y = -12 Now try the other answers to see which one works for BOTH equations!