Add: 1/2(x+4)+1/4(4x−2) . Answer should be in mixed number form.
To solve this expression, let's distribute the fractions first:
1/2 × (x + 4) = (1/2)x + (1/2) × 4 = (1/2)x + 2
1/4 × (4x - 2) = (1/4) × 4x - (1/4) × 2 = x - (1/2)
Now, let's simplify the expression by adding the like terms:
(1/2)x + 2 + x - (1/2)
= (1/2)x + x + 2 - (1/2)
= (3/2)x + 2 - (1/2)
= (3/2)x - (1/2) + 2
= (3/2)x + 3/2
Now, we can convert the improper fraction to a mixed number:
(3/2)x + 3/2 = (1 1/2)x + 1 1/2
Therefore, the expression 1/2(x + 4) + 1/4(4x - 2) in mixed number form is (1 1/2)x + 1 1/2.
To add the given expression: 1/2(x+4)+1/4(4x−2), we need to simplify each term separately and then combine them.
Step 1: Simplify the first term.
1/2(x+4) can be expanded using the distributive property:
1/2 * x + 1/2 * 4 = 1/2x + 2
Step 2: Simplify the second term.
1/4(4x−2) can also be expanded using the distributive property:
1/4 * 4x - 1/4 * 2 = x - 1/2
Step 3: Combine the simplified terms.
Now we can combine the simplified terms:
1/2x + 2 + x - 1/2
Step 4: Combine like terms.
The x terms can be combined as they have the same variable:
1/2x + x = 3/2x
The constant terms can also be combined:
2 - 1/2 = 3/2
Step 5: Write the final answer in mixed number form.
So the final expression, in mixed number form, is:
3/2x + 3/2
To add the expression 1/2(x+4) + 1/4(4x−2) and represent the answer in mixed number form, follow these steps:
Step 1: Distribute the coefficients outside the parentheses:
= 1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Step 2: Simplify each term:
= 1/2 * x + 2/2 + 4/4 * x - 2/4
Step 3: Combine like terms:
= 1/2 * x + 2/2 + 4/4 * x - 1/2
Step 4: Convert the fractions to a common denominator, which is 2:
= (1/2)x + 2/2 + (4/4)x - (1/2)
Step 5: Simplify further:
= (1/2)x + 1 + (4/4)x - 1/2
Step 6: Combine like terms:
= (1/2)x + (4/4)x + 1 - 1/2
Step 7: Add the coefficients of x:
= (1/2 + 4/4)x + 1 - 1/2
Step 8: Add the fractions:
= (2/4 + 4/4)x + 1 - 1/2
Step 9: Combine the numerators of the fractions:
= (6/4)x + 1 - 1/2
Step 10: Simplify:
= (3/2)x + 1 - 1/2
Step 11: Find a common denominator, which is 2:
= (3/2)x + (2/2) - (1/2)
Step 12: Combine the numerators of the fractions:
= (3/2)x + 1/2
Therefore, the sum of 1/2(x+4) + 1/4(4x−2) in mixed number form is (3/2)x + 1/2.