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Solving Linear Equations Linear Equations • Equations like y=x+5 3a + 2d – f = 7 • When the solutions of linear equations are graphed, they make a line The Plan • This thrilling lesson focuses on solving for single variables with Addition x + 5 = 17 Subtraction w–4=8 Division k3=4 Multiplication q 2 = 24 What is a Variable? • Simple – it’s a symbol that represents a quantity • Variables are often letters like: x, y, and z Any symbol can be used as a variable What is a Variable • In the equations: x–5=2 x–4=8 x3=4 x 2 = 24 The variable is x Solving for Variables Given an equation with one variable, it is possible to find the variable algebraically i.g., You can find the value of x that makes “x + 4 = 8” true Solving for Variables To solve for a variable isolate it to one side of the = sign Equation • x+5=8 X=8-5 • x–7=2 X=2+7 • x2=3 X=3x2 • x3=9 X=9/3 Noticing Patterns Isolating a variable is easy…if you know how Do you notice any patterns between these equations and the previous? Equation Isolated Variable Equation • x+3=8 x=8–3 • x–5=2 x=2+5 • x2=8 x=82 • x 3 = 12 x = 12 3 Addition Equations Equation Isolated Variable x+5=8 x+5–5=8–5 x+4=0 x+4–4=0–4 x + 9 = 15 x + 9 – 9 = 15 – 9 x+35 x+3–35–3 x+1=8 x+1–1=8–1 x+55 x+5–55–5 To isolate variables in addition equations, subtract the number on the variable side from both sides of the equation Subtraction Equations Equation Isolated Variable x–5=8 x–5+5=8+5 x–4=0 x–4+4=0+4 x – 9 = 15 x – 9 + 9 = 15 + 9 x–35 x–3+35+3 x–1=8 x–1+1=8+1 x–55 x–5+55+5 To isolate variables in subtraction equations, add the number on the variable side to both sides of the equation Division Equations Equation Isolated Variable x 5 = 15 x 5 5 = 15 5 x 4 = 16 x 4 4 = 16 4 x9=0 x99=09 x36 x3363 x18 x1181 x5=5 x55=55 To isolate variables in multiplication equations, divide the number on the variable side from both sides of the equation Multiplication Equations Equation Isolated Variable x5=3 x55=35 x4=0 x44=04 x91 x9919 x3=6 x33=63 x18 x1181 x5=5 x55=55 To isolate variables in division equations, multiply the number on the variable side to both sides of the equation Recognizing Patterns Operation Opposite + – – + Equation Isolated Variable Equation x+3=8 x=8–3 x–5=2 x=2+5 x2=8 x=82 x 3 = 12 x = 12 3 Recognizing Patterns Operation Opposite • Use the opposite of an + – operation with – + the number to isolate the variable Equation Isolated Variable Equation x+3=8 x=8–3 x–5=2 x=2+5 x2=8 x=82 x 3 = 12 x = 12 3 Review • Variables are symbols used to represent a quantity • To solve for variables, first isolate them • Isolate variables by doing the opposite operation on them to both sides of the = sign • Equations are fun! Additional Equations Addition Click mouse to see answers x + 6 = 12 x = 12 – 6 x+58 x8–5 x+2=9 x=9–2 x+3=8 x=8–3 x+06 x6–0 x+4<5 x<5–4 x + 5 = -2 x = -2 – 5 x+60 x0–6 x + 45 = 4 + 11 x = 15 – 45 x + 2 + 12 4 + 6 x 10 – 14 Additional Equations Click mouse to see answers Subtraction x–6=5 x=5+6 x–5<8 x<8+5 x–2=9 x=9+2 x – 3 = 19 x = 19 + 3 x–0=7 x=7+0 x–65 x5+6 x – 5 = -2 x = -2 + 5 x–6=0 x=0+6 x – 45 = 8 + 11 x = 19 + 45 x – 2 – 12 < 4 + 7 x < 11 + 14 Additional Equations Click mouse to see answers Division x 6 = 12 x = 12 6 x 5 = 10 x = 10 5 x 2 = 16 x = 16 2 x3<3 x<33 x1=6 x=61 x 4 = 20 x = 20 4 x 5 -3 x -3 5 x6=0 x=06 x 3 = 15 x = 15 3 x 2 10 x 10 2 Additional Equations Click mouse to see answers Multiplication x 6 = 12 x = 12 6 x 5 10 x 10 5 x 2 16 x 16 2 x3=3 x=33 x1=6 x=61 x 4 < 20 x < 20 4 x 5 = -15 x = -15 5 x6=0 x=06 x 3 = 15 x = 15 3 x 2 10 x 10 2 THE END

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Solving Linear Equations, linear equation, linear equations, Solving equations, how to, one side, sides of an equation, the matrix, other side, equation solving

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posted: | 4/21/2011 |

language: | English |

pages: | 20 |

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