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Linear Equations with Different Kinds of Solutions

Linear Equations with Different Kinds of Solutions. Focus 9 - Learning Goal: The students will be able to set up and solve linear equations in one variable. Solve: 11 + 3x – 7 = 6x + 5 – 3x. First, combine like terms. 11 + 3x – 7 = 6x + 5 – 3x 4 + 3x = 3x + 5

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Linear Equations with Different Kinds of Solutions

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  1. Linear Equations with Different Kinds of Solutions

  2. Focus 9 - Learning Goal: The students will be able to set up and solve linear equations in one variable.

  3. Solve: 11 + 3x – 7 = 6x + 5 – 3x • First, combine like terms. • 11 + 3x – 7 = 6x + 5 – 3x • 4 + 3x = 3x + 5 • -3x -3x . • 4 = 5 • Is this true? Does 4 really equal 5? • Then the “solution” is “no solution.” Next, subtract 3x from both sides.

  4. Solve: 6x + 5 – 2x = 4 + 4x + 1 • First combine like terms: • 6x + 5 – 2x = 4 + 4x + 1 • 4x + 5 = 5 + 4x • -4x -4x • 5 = 5 • Is this true? Does 5 really equal 5? • This means that you could put ANY number in for x and it would work. It has MANY solutions. Next, subtract 4x from both sides.

  5. Try it: Substitute in 1, then 6, then 10 for “x” and see if it works. x = 1 4x + 5 = 5 + 4x 4(1) + 5 = 5 + 4(1) 4 + 5 = 5 + 4 9 = 9 True x = 6 4x + 5 = 5 + 4x 4(6) + 5 = 5 + 4(6) 24 + 5 = 5 + 24 29 = 29 True x = 10 4x + 5 = 5 + 4x 4(10) + 5 = 5 + 4(10) 40 + 5 = 5 + 40 45 = 45 True There are Infinitely Many Solutions to this equation.

  6. Solve: 2(3 – 6m) = -30 • First, use the distributive property. • 2(3 – 6m) = -30 • 6 – 12m = -30 • -6 -6 • -12m = -36 • -12 -12 • m = 3 • There is only ONE solution to this equation. Multiply 3 and (-6m) by 2. Subtract 6 from both sides. Divide by -12.

  7. How many solutions can an equation have? x + 4 = 7 -4 -4 x = 3 One Solution x + 1 = x -x -x 1 = 0 No Solution x + 2 = 2 + x -x -x 2 = 2 Many Solutions

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