Select each pair of expressions that are equivalent. 3x + 14 – x + 112 and 4x + 134 2 + 6x and 2(3x + 1) 3(x + 1) – (1 – x) and 2x + 3 3x and 4(x + 1) – x – 4 5.5 + 2.2x + 3.8x – 4.1 and 1.4 + 6x

Options (2), (4) and (5)

Step-by-step explanation:

Option 1

(3x + 14 - x + 112) and (4x + 134)

Since, (3x + 14 - x + 112) = (3x - x) + (12 + 112)

                                      = 2x + 124

Therefore, (3x + 14 - x + 112) ≠ (4x + 134) [Not equivalent]

Option 2

(2 + 6x) and 2(3x + 1)

2(3x + 1) = (6x + 2)

Therefore, (2 + 6x) = (6x + 2) [Equivalent]

Option 3

3(x + 1) - (1 - x) and (2x + 3)

Since, 3(x + 1) - (1 - x) = 3x + 3 + x - 1

                                  = (3x + x) + (3 - 1)

                                  = 4x + 2

Therefore, (2x + 3) ≠ (4x + 2) [Not equivalent]

Option 4

3x and 4(x + 1) - x - 4

Since, [4(x + 1) - x - 4] = 4x + 4 - x - 4

                                   = (4x - x) + (4 - 4)

                                   = 3x

Therefore, 3x = [4(x + 1) - x - 4] [Equivalent]

Option 5

(5.5 + 2.2x + 3.8x - 4.1) and (1.4 + 6x)

Since, (5.5 + 2.2x + 3.8x - 4.1) = (2.2x + 3.8x) + (5.5 - 4.1)

                                                 = (6x + 1.4)

Therefore, (1.4 + 6x) = (6x + 1.4) [Equivalent]

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step-by-step explanation: