Question

Solve the linear equation: 3.4 + 2(9.7 – 4.8x) = 61.2 What are the possible steps involved in solving this equation? Check all that apply. Add 3.4 and 2. Distribute 2 to 9.7 and −4.8x. Combine 3.4 and 19.4. Divide both sides by 22.8. Subtract 22.8 from both sides. Divide both sides by −9.6.

Answer 1

Answer:

• Distribute 2 to 9.7 and −4.8x.
• Combine 3.4 and 19.4.
• Subtract 22.8 from both sides.
• Divide both sides by −9.6

Step-by-step explanation:

Here is the recommended solution method:

  3.4 + 2(9.7 – 4.8x) = 61.2 . . . . . given

  3.4 + 19.4 - 9.6x = 61.2 . . . . . . . distribute 2 to 9.7 and -4.8x

  22.8 - 9.6x = 61.2 . . . . . . . . . . . . combine 3.4 and 19.4

  -9.6x = 38.4 . . . . . . . . . . . . . . . . . subtract 22.8 from both sides

  x = -4 . . . . . . . . . . . . . . . . . . . . . . divide both sides by -9.6

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Alternate solution method using different steps

You can also "undo" what is done to the variable, in reverse order. The variable has these operations performed on it:

• multiply by -4.8
• add 9.7
• multiply that sum by 2
• add 3.4 to the product

So, another possible solution method is this:

  3.4 + 2(9.7 – 4.8x) = 61.2 . . . . . given

  2(9.7 -4.8x) = 57.8 . . . . . . . . . . . add the opposite of 3.4 (undo add 3.4)

  9.7 -4.8x = 28.9 . . . . . . . . . . . . . divide by 2 (undo multiply by 2)

  -4.8x = 19.2 . . . . . . . . . . . . . . . . . add the opposite of 9.7 (undo add 9.7)

  x = -4 . . . . . . . . . . . . . . . . . . . . . . divide by -4.8 (undo multiply by -4.8)

Answer 2

Answer:

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2. Distribute 2 to 9.7 and −4.8x.

3. Combine 3.4 and 19.4.

5. Subtract 22.8 from both sides.

6. Divide both sides by −9.6.

Step-by-step explanation: