6.4 Solving Linear Inequalities by Using Addition and Subtraction
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1 6.4 Solving Linear Inequalities by Using Addition and Subtraction
2 Solving EQUATION vs. INEQUALITY EQUATION INEQUALITY To solve an inequality, we USE THE SAME STRATEGY AS FOR SOLVING AN EQUATION: ISOLATE the variable by ADDING to or SUBTRACTING from each side of the inequality.
3 Example 1: 6.2 x 4.5 a) Solve the inequality b) Verify the solution c) Graph the solution b) The solution of the inequality 10.7 x is all numbers greater than or equal to 10.7 Choose several numbers greater than 10.7 Substitute x = in the original inequality. Left side: Right side: Does the answer SATISFIES the INEQUALITY? (i.e. Does the answer MAKE SENSE?)
4 Example 1: 6.2 x 4.5 a) Solve the inequality b) Verify the solution c) Graph the solution c) Graph the solution on a number line.
5 Example 2: 6 > x + 4 a) Solve the inequality b) Verify the solution c) Graph the solution b) The solution of the inequality 2 > x is all numbers smaller than 2 Choose several numbers smaller than 2 Substitute x = in the original inequality. Left side: Right side: Does the answer SATISFIES the INEQUALITY? (i.e. Does the answer MAKE SENSE?)
6 Example 2: 6 > x + 4 a) Solve the inequality b) Verify the solution c) Graph the solution c) Graph the solution on a number line.
7 Example 3: Jake plans to board his dog while he is away on vacation. Boarding house A charges $90 plus $5 per day. Boarding house B charges $100 plus $4 per day. For how many days must Jake board his dog for boarding house A to be less expensive than boarding house B? a) Choose a variable and write an inequality that can be used to solve this problem.
8 Example 3: Jake plans to board his dog while he is away on vacation. Boarding house A charges $90 plus $5 per day. Boarding house B charges $100 plus $4 per day. For how many days must Jake board his dog for boarding house A to be less expensive than boarding house B? a) Choose a variable and write an inequality that can be used to solve this problem. a) Let d represent the number of days Jake boards his dog. For house A: $90 + $5/day can be written, in dollars, as: For house B: $100 + $4/day can be written, in dollars, as: For house A to be less expensive than house B, $90 + $5/day must be less than $100 + $4/day So, an inequality is:
9 Example 3: Jake plans to board his dog while he is away on vacation. Boarding house A charges $90 plus $5 per day. Boarding house B charges $100 plus $4 per day. For how many days must Jake board his dog for boarding house A to be less expensive than boarding house B? a) Choose a variable and write an inequality that can be used to solve this problem d < d Boarding house A is less expensive if Jake leaves his dog there for less than 10 days.
10 Example 3: Jake plans to board his dog while he is away on vacation. Boarding house A charges $90 plus $5 per day. Boarding house B charges $100 plus $4 per day. For how many days must Jake board his dog for boarding house A to be less expensive than boarding house B? a) Choose a variable and write an inequality that can be used to solve this problem. d < 10
11 Example 4: Joel currently has a balance of $ in his bank account. He must maintain a minimum balance of $750 in the account to avoid paying a monthly fee. How much money can Joel deposit into his account to avoid paying this fee? a) Choose a variable and write an inequality that can be used to solve this problem.
12 Example 4: Joel currently has a balance of $ in his bank account. He must maintain a minimum balance of $750 in the account to avoid paying a monthly fee. How much money can Joel deposit into his account to avoid paying this fee? a) Choose a variable and write an inequality that can be used to solve this problem. a) Let d represent the number of dollars Joel can deposit to avoid paying the fee Current Balance: Minimum Balance to avoid fees: To reach the Minimum Balance to avoid fees, Joel needs to deposit d number of dollars to the Current Balance So, an inequality is:
13 Example 4: Joel currently has a balance of $ in his bank account. He must maintain a minimum balance of $750 in the account to avoid paying a monthly fee. How much money can Joel deposit into his account to avoid paying this fee? a) Choose a variable and write an inequality that can be used to solve this problem d 750
14 6.4 HOMEWORK Page: Problems: 4 14
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