Add: 1/2 ( x + 4 ) + 1/4 ( 4 x − 2 )

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

3 answers

To add the expressions 12(x+4)+14(4x2), we first simplify each term separately.

  1. Simplifying 12(x+4): 12(x+4)=12x+124=12x+2

  2. Simplifying 14(4x2): 14(4x2)=144x142=x12

Now, we can add the two results together: (12x+2)+(x12)

Combine like terms:

  • The x terms: 12x+x=12x+22x=32x

  • The constant terms: 212=20.5=1.5=32

Therefore, the combined result is: 32x+32

To express this in mixed number form, we can factor out 32: 32(x+1)

Thus, the final answer is: 32(x+1)

no

Apologies for any confusion in my previous response. Let's go through the problem step-by-step again and find the correct answer.

We want to simplify the expression:

12(x+4)+14(4x2)

  1. Distribute the terms in the parentheses:

    • For 12(x+4): 12x+124=12x+2
    • For 14(4x2): 144x142=x12
  2. Combine the results: (12x+2)+(x12)

  3. Combine like terms:

    • Combine the x terms: 12x+x=12x+22x=32x
    • Combine the constant terms: 212=20.5=1.5=32
  4. Final expression: Now we have: 32x+32

  5. Expressing in mixed number form: This expression can be factored if necessary, but in mixed number form for the term 32, you can express it as 112. So the entire expression can be written as: 32(x+1)

However, if you wish to give just the constant part in mixed number format, the result is: 32x+112

If there was any specific part of the question I misunderstood or any specific aspect of the mixed number format you wanted, please let me know!