Section 6.5 Solving Linear Inequalities Part 2

SECTION 6.5SOLVING LINEAR INEQUALITIESPART 2,

REVIEW: SOLVE THE FOLLOWING INEQUALITIES

Subtract “5x”from both sides

Add “24” toboth sides

Divide 4 from both sides

Subtract “9x”from both sides

Subtract “16”from both sides

Divide -1 from both sides

We subtracted “5x” instead| of “9x” because we want tokeep the coefficient of “x”positive when dealingwith inequalities

Suppose we didn’t keep thecoefficient of “x” positive andsubtracted “9x”

When we divide both sides bya negative value, the inequalitysign will switch sides

Divide 4 from both sides

SAMEANSWER!!

I) MULTIPLYING & DIVIDING WITH INEQUALITIES

When multiplying and dividing by a positive value,the inequality sign does not change sides

Likewise, adding or subtracting a positive/negativevalue does not change the sides of the inequality

HOWEVER, when multiplying and dividing by anegative value, the inequality sign will change sides

The sign stays thesame and faces left

The sign also staysthe same and facesright

The sign will changesides because it’sdivided by a negative value

EX: SOLVE THE FOLLOWING INEQUALITIES AND DRAWA NUMBER LINE TO REPRESENT THE SOLUTION

Subtracting a value does notchange the inequality sign

The sign will changesides because it’sdivided by a negative value

PRACTICE: GIVEN EACH EQUATION ON THE LEFT, INDICATEWHICH NUMBER LINE ON THE RIGHT IS THE CORRECT SOLUTION:

BILL HAS TWO PHONE PLANS TO CHOOSE FROM. ROGERSCHARGES $25/MONTH AND $0.10 PER MINUTE. BELL CHARGES$10/MONTH AND $0.15P PER MINUTE. LET “M” BE THE NUMBEROF MINUTES.A) WRITE AN EQUATION FOR HOW MUCH EACH PLAN COSTSB) FOR HOW MANY MINUTES WILL THE PLAN FROM ROGERS BEMORE EXPENSIVE?C) AFTER HOW MANY MINUTES WILL THE PLAN FROM BELL BEMORE EXPENSIVE?