Solving Compound Inequalities

Compound Inequality – two inequalities connected by and or or.

Solving Compound Inequalities Writing Compound Inequalities “and” type“or” type

Solving Compound Inequalities Solving a Compound Inequality with AND Isolate the variable between the two inequality symbols. What you do to one, you have to do to all three. Example:

Solving Compound Inequalities Solving a Compound Inequality with AND Isolate the variable between the two inequality symbols. What you do to one, you have to do to all three. Example: Subtract 3 from all three-4 < 2x ≤ 10 Divide all parts by 2-2 < x ≤ 5

Solving Compound Inequalities Solving a Compound Inequality with OR A solution of either part is a solution of the inequality. Solve each part separately. Example:

Solving Compound Inequalities Solving a Compound Inequality with OR A solution of either part is a solution of the inequality. Solve each part separately. Example: 2x < -2 x < -1 3x > 3 x > 1 x 1

Solving Compound Inequalities Reversing both Inequality Symbols Isolate the variable between the two inequality symbols If you multiply or divide by a negative number, you must remember to reverse the inequality symbols Example:

Solving Compound Inequalities Reversing both Inequality Symbols Isolate the variable between the two inequality symbols If you multiply or divide by a negative number, you must remember to reverse the inequality symbols Example: 12 ≤ -x < ≥ x > -15 Rewrite in order from least to greatest: -15 < x ≤ 12

Modeling Real-Life Situations Problem Solving Strategy 1. Understand the problem 2. Make a plan to solve the problem 3. Carry out the plan and solve the problem 4. Check to see if your answer is reasonable

Modeling Real-Life Situations Problem Solving Strategies Guess, check, and revise – Used when you do not have enough information Draw a diagram – Used when words describe a picture Make a table or an organized list – Used when you have data or choices to organize Use an equation or formula – Used when you know a relationship between quantities

Modeling Real-Life Situations Problem Solving Strategies Use a proportion – Used when you know two ratios are equal Look for a pattern – Used when you can examine several cases Break the problem into simpler parts – Used when you have a multi-step problem Solve a simpler problem – Used when easier numbers help you understand a problem Work backward – Used when you are looking for a fact leading to a known result