6-3B Solving Multi-Step Inequalities Algebra 1 Glencoe McGraw-HillLinda Stamper

A multi-step inequality is solved by transforming the inequality more than one time. Undo addition or subtraction before undoing multiplication or division or you may make the problem more complicated to solve. Always remember the basic rule when isolating the variable: Solving Multi–Step Inequalities Whatever you do to one side of the inequality sign, you must also do to the other side of the inequality sign.

To solve inequalities that have variables on both sides of the inequality symbol, first collect the variable terms on one side. Solve. Write the problem. Collect variable terms on one side. Undo addition and simplify. Undo multiplication and simplify.

To solve inequalities that have variables on both sides of the inequality symbol, first collect the variable terms on one side. Solve. Write the problem. Collect variable terms on one side. Undo addition and simplify. Undo multiplication and simplify. < /

When solving inequalities that contain grouping symbols, first use the distributive property. Write problem. Distribute and combine like terms. Collect variable terms on one side. Isolate the variable using inverse operations.

Solve. Leave the fraction improper. It must be in lowest terms. Example 1 Example 2 Example 3 Use good form – place the negative out front! > /

If solving an inequality results in a statement that is always true, the solution is the set of all real numbers. If solving an inequality results in a statement that is never true, the solution is an empty set, written as .

Write problem. Distribute and combine like terms. Collect variable terms on one side. Result is a false statement. Copy in your spiral notebook! 

Write problem. Distribute and combine like terms. Collect variable terms on one side. Result is a true statement. Copy in your spiral notebook! all real numbers

Write problem. Distribute and combine like terms. Collect variable terms on one side. Result is a true statement. all real numbers Subtract 24 from each side. Be sure to simplify the inequality to determine whether it is a true statement. If the inequality is true, the solution is the set of all real numbers. If the inequality is false, the solution is the empty set, written as .

Solve. > / < /



all real numbers

7) One half of a number increased by one is greater than or equal to six less than one fourth of the number. Write an inequality and then solve.

8) Sixteen more than three fourths of a number is more than one eighth of the number less than Write an inequality and then solve.

6-A4 Pages 311–312 #26–33, 39–42, 44–47.