Add: 12(x+4)+14(4x−2) . Answer should be in mixed number form

Answer 1

To simplify the expression, we multiply each term inside the parentheses:

12(x + 4) becomes 12x + 48

14(4x - 2) becomes 56x - 28

Now we can add the like terms:

12x + 48 + 56x - 28

Combine the x-terms by adding the coefficients:

12x + 56x = 68x

Combine the constant terms:

48 - 28 = 20

Therefore, the simplified expression is 68x + 20.

Since the answer is not a fraction, we can write it as a mixed number with zero as the whole number part:

0 68/1 + 20/1

Converting both fractions to a common denominator of 1:

0 68/1 + 20/1 = 0 * 1/1 + 68/1 + 20/1

Combining the fractions:

0 * 1/1 + 68/1 + 20/1 = 0 + 68 + 20/1

Adding the whole number and fractions separately:

0 + 68 + 20/1 = 68 + 20/1

Therefore, the answer in mixed number form is 68 + 20.

Answer 2

Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form

Answer 3

To solve this expression, we can start by distributing the fractions to the terms inside the parentheses:

1/2(x + 4) = 1/2 * x + 1/2 * 4 = 1/2x + 2/2 = 1/2x + 1

1/4(4x - 2) = 1/4 * 4x + 1/4 * (-2) = 1x - 1/2

Now we can add the like terms:

1/2x + 1 + 1x - 1/2

Combine the x-terms by adding the coefficients:

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

Combine the constant terms:

1 - 1/2 = 2/2 - 1/2 = 1/2

Therefore, the simplified expression is 3/2x + 1/2.

To convert this expression to a mixed number form, we divide the coefficient of x (3/2) by the denominator (2) and write the quotient as the whole number part, while the remainder becomes the new numerator:

3/2 ÷ 2 = 1 remainder 1

So the mixed number form of the expression is 1 1/2.