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Inequality

Absolute value notes

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1-4, 1-6 Solving Absolute Value Equations and Inequalities Absolute value: distance from zero on a number line. Since distance in a nonnegative, the absolute value of a number is always positive. The symbol lxi is used to represent the absolute value of a number x. I units 4 units I I I I 1 I 3 4 5 Solving Absolute Value Equations: For any real numbers a and b, where b ~! 0, if Jal = then a = b or ?a = b. The second case is often written as a = ?b. Steps 1. Isolate the Absolute Value expression 2. Rewrite equation without the I I symbols. a. One with positive answer b. One with negative answer Ex 1: Jx-51=7 x-c3- ?t-3 k'3 + 3. Solve each equation '7 2\: flL1 - '7 I 2 - \ - 4. Check your answers (plug back into I T

Algebra Fill In Notes 2.6

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02.06 Compound Inequalities Essential Questions How can you create inequalities in one variable and use them to solve problems? How can you represent constraints by inequalities? How can you interpret solutions as viable or nonviable options in a modeling context? Absolute Value Inequalities: Absolute Value Inequalities are problems that involve ranges. For example: On public stairs, handrails must be installed. The height of the handrails must be within a 3 inch range of 35 inches. Compound inequality Key words ?and? / ?or? Scenario 1 A fish has to measure between 18 and 24 inches in length. b>= 18 and b<=24 Writing the compound inequality like this makes it easier to understand that the solutions for b must fall between 18 and 24 inches Scenario 2

Algebra Fill In Notes 2.5

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02.05 Inequalities Essential Questions How can you create inequalities in one variable and use them to solve problems? How can you solve linear inequalities in one variable? An?inequality?means the value of the variable is not equal to one number (like in equations), but instead may be greater than or less than a number. There are four primary symbols you need to know when working with inequalities. Indicate what type of circle goes with each inequality symbol > Greater than ______________ < Less than _______________ ? Greater than or equal to ________________ ? Less than or equal to ________________ When you graph an inequality on a number line, there are two questions you must answer. Open or closed circle

Two step equations and inequalities

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It takes two steps to solve an equation or inequality that has more than one operation: Simplify using the inverse of addition or subtraction. Simplify further by using the inverse of multiplication or division. Remember, when you multiply or divide an inequality by a negative number, you must reverse the inequality symbol.

Inequalities

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The only difference between the linear equation "x + 3 = 2" and this linear inequality is that I have a "less than" sign, instead of an "equals" sign. The solution method is exactly the same: subtract 3 from either side. Note that the solution to a "less than, but not equal to" inequality is graphed with a parentheses (or else an open dot) at the endpoint, indicating that the endpoint is not included within the solution. Note that "x" in the solution does not "have" to be on the left. However, it is often easier to picture what the solution means with the variable on the left. Don't be afraid to rearrange things to suit your taste. 3) 4x + 6 >= 3x ? 5, then x <= ?11 -2x > 4, then x < -2 Graphically, the solution is: graphical solution

Inequalities Signs

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You know you flip the inequality sign when you divide or multiply be a negative. 3(x-1)<12 when you solve you get x<5 but if you changed the 3 to a -3 the solution would become x>-5 where you would flip the sign from < to >

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