Add: 1/2(x+4)+14(4x−2) . Answer should be in mixed number form
To simplify the expression, let's start by distributing the 14 to both terms inside the parentheses:
1/2(x + 4) + 14(4x - 2)
= 1/2 * x + 1/2 * 4 + 14 * 4x - 14 * 2
= 1/2 * x + 2/2 + 56x - 28
Combining like terms, we have:
= 1/2 * x + 56x - 26
Now, let's find a common denominator to rewrite the expression:
= (1/2 * x + 56x - 26) * 2/2
= (x/2 + 112x - 52)/2
Lastly, let's simplify the expression by dividing each term by 2:
= x/4 + 56x/2 - 52/2
= x/4 + 28x - 26
Therefore, the simplified expression in mixed number form is: x/4 + 28x - 26.
are you sure
Apologies for the mistake. Let's simplify the expression correctly:
1/2(x + 4) + 14(4x - 2)
= 1/2 * x + 1/2 * 4 + 14 * 4x - 14 * 2
= 1/2 * x + 2/2 + 56x - 28
= 1/2 * x + 56x - 26
To convert the expression into mixed number form, we need to find a common denominator for the fractions. The common denominator is 2. Then, we can rewrite the expression as follows:
= (1/2 * x + 56x - 26) * 2/2
= (x/2 + 112x/2 - 26) * 2/2
= (x + 112x - 26)/2
In mixed number form, the expression is:
= (113x - 26)/2
wrong
Apologies for the mistake. Let's simplify the expression correctly:
1/2(x + 4) + 14(4x - 2)
First, let's distribute 1/2 to (x + 4):
(1/2)(x + 4) + 14(4x - 2)
= (1/2)x + (1/2)4 + 14(4x - 2)
= (1/2)x + 2 + 14(4x - 2)
= (1/2)x + 2 + 56x - 28
Next, let's combine like terms:
= (1/2)x + 56x - 26
To convert the expression into mixed number form, we need to find a common denominator for the fractions. The common denominator is 2. Then, we can rewrite the expression as follows:
= (1/2)x + (112x/2) - (26/2)
= (1/2)x + (112x - 26)/2
In mixed number form, the expression is:
= (x/2) + (112x - 26)/2
Therefore, the simplified expression in mixed number form is: (x/2) + (112x - 26)/2.
To simplify the expression 1/2(x+4)+14(4x−2), let's distribute the coefficients:
1/2(x+4) = 1/2 * x + 1/2 * 4 = 1/2x + 2
14(4x−2) = 14 * 4x - 14 * 2 = 56x - 28
Now we can combine like terms:
1/2x + 2 + 56x - 28
Combining the x terms and the constant terms, we get:
(1/2x + 56x) + (2 - 28)
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 2:
(1/2x + 56x) + (2 - 28) = (1/2x) + (112x/2) + (-26/2) = (1/2x + 112x/2 - 26/2)
Now, let's simplify further:
(1/2x + 112x/2 - 26/2) = (1/2x + 56x - 26)/2
Finally, if we divide both the numerator and denominator by 2, we get:
(1/2x + 56x - 26)/2 = 1/2x + 56x/2 - 26/2 = 1/2x + 28x - 13
So, the simplified expression in mixed number form is 1/2x + 28x - 13.
To add the expression 1/2(x+4) + 14(4x-2) and represent the answer in mixed number form, you can follow these steps:
Step 1: Distribute the 14 to each term inside the parentheses:
1/2(x+4) + 14(4x-2) = 1/2(x+4) + (14*4x - 14*2)
Simplifying further:
= 1/2(x+4) + (56x - 28)
Step 2: Distribute the 1/2 to each term inside the parentheses:
= (1/2*x + 1/2*4) + (56x - 28)
= (1/2*x + 2) + (56x - 28)
Step 3: Combine like terms:
= 1/2x + 2 + 56x - 28
= (1/2x + 56x) + (2 - 28)
= (57/2)x - 26
Step 4: Convert the final answer to mixed number form:
To convert the fraction (57/2) into a mixed number, divide the numerator (57) by the denominator (2):
57 ÷ 2 = 28 remainder 1
So, the mixed number form of (57/2) is 28 1/2.
Therefore, the final answer in mixed number form is:
28 1/2x - 26