Presentation on theme: "Daily Quiz - Simplify the expression, then create your own realistic scenario for the final expression."— Presentation transcript:
1Daily Quiz -Simplify the expression, then create your own realistic scenario for the final expression.
2Simplify Expression Check Complete in your notes as Practice!Multiply the quantity by (-5) and add the product to the quantity
3Objectives: SWBAT… Create and carry out a plan for solving equations Maintain equality when solving equations through inverse operations and simplification techniques (such as combining like terms)Solve one-step linear equationsSolve multi-step linear equations
4Review of Key ConceptsA variable is a letter which represents an unknown number. Any letter can be used as a variable.An algebraic expression contains at least one variable.Examples: a, x+5, 3y – 2zA verbal expression uses words to translate algebraic expressions.Example:“The sum of a number and 3” represents “n+3.”An equation is a sentence that states that two mathematical expressions are equal.Linear Equation in One Variable - can be written in the form ax +b =c, a 0Example: 2x-16=18
5Key Concepts Continued To solve means to find the value of a variableInverse Operations are operations that “undo” each otherdivision and multiplicationaddition and subtractionIsolate a Variable is part of the process of solving, in which the variable is placed on one side of the equation by itselfEquality is the state of being equal or having the same value – we always maintain equality when solving equationsA solution is a value that can take the place of a variable to make an equation true
6Single-Step Linear Equation Solving equations is just a matter of undoing operations that are being done to the variable. In a simple equation, this may mean that we only have to undo one operation, as in the following example. Solve the following equation for x x + 3 = 8x + 3 = the variable is xx + 3 – 3 = 8 – 3 we are adding 3 to the variable, so to get rid of the added 3, we do the opposite subtract 3.x = remember to do this to both sides of the equation.
7We start with the operation the farthest away from the variable! Multi-Step Linear EquationIn an equation which has more than one operation, we have to undo the operations in the correct order.We start with the operation the farthest away from the variable!Solve the following equation: 5x – 2 =135x – 2 = The variable is x5x – = We are multiplying it by 5, and subtracting 2First, undo the subtracting by adding 2.5x = Then, undo the multiplication by dividing by 5.x = 3
8Steps to Solving Equations Simplify each side of the equation, if needed, by distributing or combining like terms.Move variables to one side of the equation by using the opposite operation of addition or subtraction.Isolate the variable by applying the opposite operation to each side.First, use the opposite operation of addition or subtraction.Second, use the opposite operation of multiplication or division.Check your answer.
9How can we “undo” operations? Isn’t this wrong? Addition Property of Equality – states you can add the same amount to both sides of an equation and the equation remains true = = = 9 ? true Subtraction Property of Equality – states you can subtract the same amount from both sides of an equation and the equation remains true = – 3 = 11 – = 8 ? true
10Example5(3 + z) – (8z + 9) = – 4z15 + 5z – 8z – 9 = – 4z (Use distributive property)6 – 3z = – 4z (Simplify left side)6 – 3z + 4z = – 4z + 4z (Add 4z to both sides)6 + z = (Simplify both sides)6 + (– 6) + z = 0 +( – 6) (Add –6 to both sides)z = – 6 (Simplify both sides)
11Multiplication Property of Equality – states you can multiply the same amount on both sides of an equation and the equation remains true.4 · 3 = 122 · 4 · 3 = 12 · 224 = 24Division Property of Equality – states you can divide the same amount on both sides of an equation and the equation remains true.12 = 62
12Example (– 1)(– y) = 8(– 1) (Multiply both sides by –1) y = – 8 (Simplify both sides)
13Example 3z – 1 = 26 3z – 1 + 1 = 26 + 1 (Add 1 to both sides) Recall that multiplying by a number is equivalent to dividing by its reciprocalExample3z – 1 = 263z – = (Add 1 to both sides)3z = 27 (Simplify both sides)(Divide both sides by 3)z = (Simplify both sides)
14Special CasesNo Solution – we arrive at an answer that does not maintain equalityInfinite – we arrive at an answer that will always maintain equality(always be true)