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Exit Level TAKS Preparation Unit Objective 4 © A Very Good Teacher 2007 Writing Equations and Inequalities • 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: 4, Ac3A No more than No less than At least At most © 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? income Salary + Commission The words “at least” Total indicate that this will be an inequality. Now write the inequality. y ≥ ? 200 + .10x Could be greater than or exactly 4, Ac3A © 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 equation Profit = 9x – (3.5x + 50(3)) 4, Ac3B © A Very Good Teacher 2007 Solving Equations and Inequalities, cont… • Now that we have an equation, we can substitute any given values Profit = 9x – (3.5x + 50(3)) • We can replace ‘profit’ with zero to find the break even point 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 27.27 = x 150 = 5.5x 5.5 5.5 4, Ac3B © 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 © 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 © 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. Total Equation Comparison Equation j + s = 12 22j + 15s = 215 4, Ac4A © 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 © 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? y = 5x - 2 A. x = -2 B. x = -1 C. x = 2 D. x = 1 4x – y = 3 4(-2) – y = 3 -8 – y = 3 +8 +8 – y = 11 y = 5(-2) - 2 y = -10 - 2 y = -12 y = -11 Now try the other answers to see which one works for BOTH equations! 4, Ac4B © A Very Good Teacher 2007