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Solving Equations Using Addition and Subtraction Cues • • • • • • • Vocabulary Balance Inverse Operations Properties of Equality Addition Properties of Equality Subtraction Ex 1 Ex 2 Solving Equations Using Subtraction Addition and Goals: 1. I can solve one step linear equations using addition and subtraction. 2. I can use linear equations to solve real-life problems such as finding a record temperature. Special Vocab (notebook please… Equation – a mathematical statement that two expressions are equal. A solution of an equation is a value of the variable that makes the equation true. To find solutions, we isolate the variable. A variable is isolated when it appears by itself (no coefficients) on one side of the equation. Solving Equations Basics When transforming equations (isolating the variable) – they must remain balanced! Whatever you do to one side of the = sign, you MUST do to the other side! Inverse Operations – are operations that undo each other, such as addition and subtraction. Inverse operations help you isolate the variable in an equation. * Do the opposite to “undo” an equation! If you are adding TO the variable – then subtract. If subtracting FROM the variable – then add. Sometimes you have to add the opposite…… If multiplying TO the variable, then divide! If DIVIDING the variable by something, then multiply by the reciprocal! Transformations that Produce Equivalent Equations Original Equation Add the same number to each side. x–3=5 Subtract the same number from each side. x + 6 = 10 Simplify one or both sides. x=8-3 Interchange the sides. 7=x Equivalent Equation Add 3 x=8 x=4 Subtract 6 Simplify x=5 x=7 Interchange Properties of Equality Addition Property of Equality – You can add the same number to both sides of an equation, and the statement will still be true. Numbers Algebra 3=3 a=b 3+2=3+2 a+c=b+c 5=5 Properties of Equality Subtraction Property of Equality – You can subtract the same number from both sides of an equation, and the statement will still be true. Numbers Algebra 7=7 a=b 7-5=7-5 a-c=b-c 2=2 Solution Steps Each time you apply a transformation to an equation, you are writing a solution step. Solution steps may be written one below each other with the equal sign aligned. Survival tip: SHOW your solution steps – it makes checking your work easier and your grade higher! This may not seem important now, but when have you much more complex equations, you will need that skill. (BTW – this is not optional). Examples – Using addition to solve x – 9 = -17 + 9 = +9 x = -8 x – 9 = -17 -8 – 9 = -17 -17 = -17 Now try….. And check: x – 12 = 13 Your turn n – 3.2 = 5.6 -6 = k - 6 Examples – Using subtraction to solve x + 12 = 15 - 12 = -12 x= 3 x +12 = 15 3 + 12 = 15 15 = 15 Now try….. And check: -5 = k +5 Your turn 1 1 d 2 2 6 t 14 Adding the Opposite -8 + b = 2 +8 +8 b = 10 -8 + b = 2 Your turn 2.3 m 7 3 1 z 1 4 4 Examples – Simplifying First -9 = n – (-4) -9 = n + 4 - 4 = -4 -13 = n -9 = n – (-4) -9 = -13 – (-4) -9 = -13 +4 -9 = -9 Your Turn -11 = n – (-2) Your turn 2 (b) 6 Real World Problem A person’s maximum heart rate, is the highest rate, in beats per minute that the person’s heart should reach. One way to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find the maximum heart rate of a 15 year old. - Then use this method to find Mr. Hedges’ age if his maximum heart rate is 168.