Add: 12(x+4)+14(4x−2)

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. Answer should be in mixed number form.(1 point)

1 answer

To solve the expression \( 12(x+4) + 14(4x−2) \), let's first distribute both terms:

  1. Distribute \( 12 \) in \( 12(x+4) \): \[ 12(x) + 12(4) = 12x + 48 \]

  2. Distribute \( 14 \) in \( 14(4x−2) \): \[ 14(4x) + 14(-2) = 56x - 28 \]

Now combine the two results: \[ 12x + 48 + 56x - 28 \]

Now, combine the like terms:

  • Combine \( 12x \) and \( 56x \): \[ 12x + 56x = 68x \]

  • Combine \( 48 \) and \( -28 \): \[ 48 - 28 = 20 \]

So we have: \[ 68x + 20 \]

Next, we can express this in mixed number form. Since \( 20 \) can be written as \( 20/1 \), we can also express \( 68x + 20 \) as: \[ 68x + 20 = 68x + \frac{20}{1} \]

This isn't needed in mixed number form. If you want to express \( 20 \) as a mixed number, it would just remain \( 20 \) since it is a whole number.

Therefore, the final answer is: \[ 68x + 20 \]

If you need it in terms of x, we can finalize: Mixed number form: \( 68x + 20 \).