Add: 1/2 (x+4) + 1/4 (4x-2). Answer should be in mixed number form.
To solve the equation and express the answer in mixed number form, we need to combine the terms and simplify.
1/2 (x + 4) + 1/4 (4x - 2)
Distribute the fractions:
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Simplify the multiplied fractions:
1/2 * x + 2 + 1x + 1/2 - 1/2
Combine like terms:
1/2 * x + 1x + 2 - 1/2 + 0
Simplify:
(1/2 + 2/2)x + (2 - 1/2)
4/2x + 3/2
Simplify the fraction:
2x + 3/2
To convert the fraction into a mixed number, we divide the numerator by the denominator:
3 ÷ 2 = 1 remainder 1
Therefore, the final answer in mixed number form is:
2x + 1 1/2
wrong
Apologies for the mistake. Let's try solving the equation correctly:
1/2 (x + 4) + 1/4 (4x - 2)
First, distribute both fractions:
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Simplify the multiplied fractions:
1/2 * x + 2/2 + 1/1 * x - 1/2
Combine like terms:
1/2x + 1 + 4/4x - 1/2
Simplify the fractions:
1/2x + 1 + x - 1/2
Combine the x terms:
1/2x + x = 3/2x
Combine the constant terms:
1 - 1/2 = 2/2 - 1/2 = 1/2
Therefore, the final answer is:
3/2x + 1/2
that is also wrong
Apologies again for the error. Let's solve the equation correctly:
1/2 (x + 4) + 1/4 (4x - 2)
First, distribute both fractions:
(1/2 * x + 1/2 * 4) + (1/4 * 4x - 1/4 * 2)
Simplify the multiplied fractions:
(1/2 * x + 2/2) + (1x - 1/2)
Combine like terms:
(1/2 * x + 1) + (1x - 1/2)
Now combine the terms with x:
1/2x + 1 + 1x - 1/2
Combining the constant terms:
1 + (-1/2) = 2/2 - 1/2 = 1/2
Therefore, the final answer is:
1/2x + 1/2
To solve the given expression, we need to combine and simplify the terms. Here's how:
Step 1: Distribute the 1/2 and 1/4 to their respective expressions inside the parentheses.
1/2 (x+4) + 1/4 (4x-2)
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
= 1/2x + 2/2 + 4/4x - 2/4
Step 2: Simplify the fractions.
= 1/2x + 1 + 1x - 1/2
= 1/2x + x - 1/2
Step 3: Combine like terms.
= 1/2x + x - 1/2
= (1/2x + x) - 1/2
= (3/2x) - 1/2
Since the answer should be in mixed number form, we can convert the improper fraction (3/2x) to a mixed number.
= 1 1/2x - 1/2
Therefore, the simplified and converted expression is 1 1/2x - 1/2.