Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form.
can you make the answer more clear??
are there answers other than 2?
To add the expression 1/2(x+4)+1/4(4x−2) and express the answer in mixed number form, follow these steps:
Step 1: Distribute and simplify
Start by distributing the fractions and simplifying any terms.
1/2(x+4) + 1/4(4x−2)
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= 1/2 * x + 2/2 + 4/4 * x - 2/4
The denominators 2, 2, and 4 are all multiples of 2, so we can convert them to a common denominator of 4:
= 1/2 * x + 2/2 + 4/4 * x - 2/4
= 2/4 * x + 2/2 + 4/4 * x - 2/4
= (2x)/4 + 2/2 + 4x/4 - 2/4
= (2x + 2 + 4x - 2)/4
= (6x)/4
= 3x/2
Step 2: Convert to mixed number form
To express the answer as a mixed number, we need to divide the numerator (3x) by the denominator (2).
3x ÷ 2
The quotient will be the whole number in the mixed number, and the remainder will be the numerator of the fraction part. Let's perform the division:
3x ÷ 2 = (3x) / (2)
Since the expression does not include specific values or constraints for x, we leave it in this form.
Therefore, the answer to the expression 1/2(x+4)+1/4(4x−2) in mixed number form is (3x/2).
To simplify the expression, we combine like terms.
1/2(x + 4) + 1/4(4x - 2)
Using the distributive property, we distribute the fractions.
(1/2 * x + 1/2 * 4) + (1/4 * 4x - 1/4 * 2)
Simplifying further:
(1/2 * x + 2/2) + (x - 1/2)
Combining like terms:
1/2x + 2/2 + x - 1/2
Now, we can combine the fractions:
1/2x + 1 + x - 1/2
To add fractions with different denominators, we need to find a common denominator. In this case, the least common denominator is 2. Therefore, we need to rewrite the fractions:
1/2x + (2/2)x + 2/2 - 1/2
Simplifying:
1/2x + 2/2x + 1 - 1/2
Now, we add the fractions with the same denominator:
(1/2x + 2/2x) + (1 - 1/2)
Simplifying the fractions:
(1/2x + x) + (1/1 - 1/2)
Adding the fractions and simplifying further:
(3/2x) + (2/2 - 1/2)
Now, we combine the fractions:
(3/2x) + (1/2)
To add the fractions, we need a common denominator. The least common denominator is 2x. Therefore, we rewrite the fractions:
(3/2x)(x/x) + (1/2)(x/x)
Expanding the denominators:
3x/2x + x/2x
Now, we combine the fractions:
(3x + x)/2x
Simplifying further:
4x/2x
Dividing the numbers:
4/2
Simplifying:
2
Therefore, the answer in mixed number form is 2.
Apologies for any confusion. To simplify the expression 1/2(x + 4) + 1/4(4x - 2) and express the answer in mixed number form:
1/2(x + 4) + 1/4(4x - 2)
Using the distributive property, we distribute the fractions:
(1/2 * x + 1/2 * 4) + (1/4 * 4x - 1/4 * 2)
Simplifying further:
(1/2 * x + 2/2) + (x - 1/2)
Combining like terms:
1/2x + 2/2 + x - 1/2
Simplifying the fractions:
1/2x + 1 + x - 1/2
Now, we rearrange the terms, grouping similar terms:
1/2x + x + 1 - 1/2
Combining the fractions with the same denominator:
(1/2x + 2/2x) + (1 - 1/2)
Simplifying the fractions:
(1/2x + x) + (1/1 - 1/2)
Adding the fractions and simplifying further:
(3/2x) + (2/2 - 1/2)
Combining the fractions:
(3/2x) + (1/2)
To add the fractions, we need a common denominator. The least common denominator is 2x. Therefore, we rewrite the fractions:
(3/2x)(x/x) + (1/2)(x/x)
Expanding the denominators:
(3x/2x) + (x/2x)
Now, we combine the fractions:
(3x + x)/2x
Simplifying further:
4x/2x
Dividing the numbers:
4/2
Simplifying:
2
Therefore, the answer to the expression 1/2(x + 4) + 1/4(4x - 2) in mixed number form is 2.
Apologies for the confusion. Let's reevaluate the expression to ensure we haven't missed any possible answers.
To simplify the expression: 1/2(x + 4) + 1/4(4x - 2)
1/2(x + 4) + 1/4(4x - 2)
Using the distributive property, we distribute the fractions:
(1/2 * x + 1/2 * 4) + (1/4 * 4x - 1/4 * 2)
Simplifying further:
(1/2 * x + 2/2) + (x - 1/2)
Combining like terms:
1/2x + 2/2 + x - 1/2
Simplifying the fractions:
1/2x + 1 + x - 1/2
Now, we rearrange the terms, grouping similar terms:
1/2x + x + 1 - 1/2
Combining the fractions with the same denominator:
(1/2x + 2/2x) + (1 - 1/2)
Simplifying the fractions:
(1/2x + x) + (1/1 - 1/2)
Adding the fractions and simplifying further:
(3/2x) + (2/2 - 1/2)
Combining the fractions:
(3/2x) + (1/2)
To add the fractions, we need a common denominator. The least common denominator is 2x. Therefore, we rewrite the fractions:
(3/2x)(x/x) + (1/2)(x/x)
Expanding the denominators:
(3x/2x) + (x/2x)
Now, we combine the fractions:
(3x + x)/2x
Simplifying further:
4x/2x
Dividing the numbers:
4/2
Simplifying:
2
After reevaluating the expression, the only possible answer is 2.
To add the given expression, follow these steps:
Step 1: Distribute the fractions
1/2(x+4) + 1/4(4x−2) becomes:
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Simplifying this, we get:
1/2x + 2/2 + x - 1/2
Step 2: Combine like terms
Combine the coefficients of 'x' and add/subtract the constants:
1/2x + x + 2/2 - 1/2
Step 3: Convert to common denominator
The least common denominator is 2, so let's convert all the fractions to have a denominator of 2:
1/2x + 2/2x + 2/2 - 1/2
Step 4: Combine the fractions
Combine the fractions with the same denominator:
(1/2x + 2/2x) + (2/2 - 1/2)
Simplifying this, we get:
(3/2x) + (1/2)
Step 5: Simplify the expression
Since the coefficient of 'x' is 3/2, we can rewrite this as a mixed number by dividing the coefficient by the denominator and expressing any remainder as a fraction:
3/2x can be written as 1 1/2x
Therefore, the simplified expression in mixed number form is:
1 1/2x + 1/2