Practice Problem 4a – 7 ≤ 17 AND 14 – a > -5a + 3 Solve the Compound Inequality AND Graph
Practice Problem Rachel is planning a wedding for 100 to 250 people, depending on costs. She has hired a caterer that charges $20 per person, plus a flat fee of $200. Write an inequality in terms of “p” that describes how many people Rachel plans to invite. Adjust the inequality to show how much the caterer will charge. What is the range of catering fees that Rachel is considering.
Solving Absolute Value Equations & Inequalities
Absolute Value (of x) Symbol lxl The distance x is from 0 on the number line. Always positive Ex: l-3l=3 -4 -3 -2 -1 0 1 2
Ex: x = 5 What are the possible values of x? x = 5 or x = -5
To solve an absolute value equation: ax+b = c, where c>0 To solve, set up 2 new equations, then solve each equation. ax+b = c or ax+b = -c ** make sure the absolute value is by itself before you split to solve.
Ex: Solve 6x-3 = 15 6x-3 = 15 or 6x-3 = -15 6x = 18 or 6x = -12 x = 3 or x = -2 * Plug in answers to check your solutions!
Ex: Solve 2x + 7 -3 = 8 Get the abs. value part by itself first! 2x+7 = 11 Now split into 2 parts. 2x+7 = 11 or 2x+7 = -11 2x = 4 or 2x = -18 x = 2 or x = -9 Check the solutions.
Solving Absolute Value Inequalities ax+b < c, where c > 0 Becomes an “and” problem Changes to: –c < ax+b < c ax+b > c, where c > 0 Becomes an “or” problem Changes to: ax+b > c or ax+b < -c
SOLVING ABSOLUTE-VALUE EQUATIONS AND INEQUALITIES means means means means means means means means means means ax b c andax b c. |ax b | c |ax b | c ax b c andax b c. When an absolute value is less than a number, the inequalities are connected by and. When an absolute ax b c orax b c. |ax b | c value is greater than a number, the inequalities are connected by or. ax b c orax b c. |ax b | c ax b c orax b c. |ax b | c