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16 May, 06:31

Transform each of the following equations to determine whether each has one solution, infinitely many solutions or no solution. Use the result of your transformation to state the number of solutions.

1. 2x + 4 = 3 (x - 2) + 1

2. 4 (x + 3) = 3x + 17

3. 3x + 4 + 2x = 5 (x - 2) + 7

4. 2 (1 + 5x) = 5 (2x - 1)

5. - 18 + 15x = 3 (4x - 6) + 3x

+5
Answers (2)
  1. 16 May, 07:11
    0
    1. 2x + 4 = 3 (x - 2) + 1

    2x + 4=3x-6+1

    2x-3x=-5-4

    -x = - 9

    x = 9 one solution

    2. 4 (x + 3) = 3x + 17

    4x + 12=3x+17

    4x-3x=17-12

    x = 5 one solution

    3. 3x + 4 + 2x = 5 (x - 2) + 7

    5x+4=5x-10+7

    5x-5x=-3-4

    0x=-7 no solution

    4. 2 (1 + 5x) = 5 (2x - 1)

    2+10x=10x-5

    10x-10x=-5-2

    0x = - 7 no solution

    5. - 18 + 15x = 3 (4x - 6) + 3x

    -18+15x=12x-18+3x

    15x-15x = - 18+18

    0 = 0 infinite solutions
  2. 16 May, 09:49
    0
    1.

    we distribute then move placeholders to get

    2x+4=4x-6+1

    9=x

    one solution

    2. distribute

    4x+12=3x+17

    x=5

    one solution

    3. distribute and combine like terms

    5x+4=5x-10+7

    4=-3

    false

    no solution

    4. distribute

    2+10x=10x-5

    2=-5

    false

    no solution

    5. distribute

    -18+15x=12x-18+3x

    x=x

    true

    infinite solutions
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