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22 March, 11:54

2. Solve each given location and show your work. Tell whether each equation has one solution, an infinite number of solutions, or no solutions. Explain your answers. (a) 4x + 2 (x - 1) = 10 + 2x (b) 30 - x = 10 - (6 + 10) (c) 8x = 4x + 4x + 10 (x-x) Answers:

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  1. 22 March, 12:18
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    a one solutions x=3

    b one solution x=36

    c infinite solutions

    Step-by-step explanation:

    (a) 4x + 2 (x - 1) = 10 + 2x

    Distribute

    4x+2x-2 = 10+2x

    Combine like terms

    6x-2 = 10+2x

    Subtract 2x from each side

    6x-2x-2 = 10+2x-2x

    4x-2 = 10

    Add 2 to each side

    4x-2+2 = 10+2

    4x=12

    Divide by 4

    4x/4 = 12/4

    x=3

    There is one solution

    (b) 30 - x = 10 - (6 + 10)

    Distribute the minus sign

    30-x = 10-6-10

    30-x=-6

    Subtract 30 from each side

    30-x-30 = - 6-30

    -x = - 36

    Multiply by - 1

    x = 36

    (c) 8x = 4x + 4x + 10 (x-x)

    Parentheses first

    8x = 4x+4x+10 (0)

    8x=4x+4x

    Combine like terms

    8x=8x

    Subtract 8x from each side

    8x-8x=8x-8x

    0=0

    This is always a true statement

    x = all real numbers

    infinite solutions
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