Add 1/2(x+4)+1/4(4x-2) answer should be in mixed number form
To simplify the expression, let's first distribute:
1/2(x+4) + 1/4(4x-2)
= 1/2 * x + 1/2 * 4 + 1/4 * 4x + 1/4 * -2
= 1/2 * x + 2 + x + -1/2
Now, let's combine like terms:
1/2 * x + x + 2 - 1/2
= (1/2 + 2/2) * x + 2 - 1/2
= 3/2 * x + 4/2 - 1/2
= (3x + 4 - 1) / 2
= (3x + 3) / 2
Therefore, the simplified expression in mixed number form is 3/2(x+1).
To simplify the expression and convert it to a mixed number form, you need to follow these steps:
Step 1: Distribute the coefficients to the terms inside the parentheses:
1/2(x+4) + 1/4(4x-2)
=(1/2)x + 1/2(4) + (1/4)4x - (1/4)2
Step 2: Simplify the terms:
=(1/2)x + 2/2 + (4/4)x - (2/4)
Step 3: Combine like terms:
=(1/2)x + (4/4)x + 2/2 - 2/4
=(1/2)x + x + 2/2 - 1/2
Step 4: Express all terms with a common denominator:
=(1/2)x + (2/2)x + (2/2) - (1/2)
=(1/2)x + (2/2)x + 4/4 - 1/2
Step 5: Add the fractions with the same denominator:
=(1/2)x + (2/2)x + 4/4 - 1/2
=(1/2)x + (2/2)x + 4/4 - 2/4
=(1/2)x + (2/2)x + 2/4
Step 6: Combine the terms with "x":
=(1/2)x + (2/2)x + 2/4
=(3/2)x + 2/4
Step 7: Convert the improper fraction to a mixed number:
The mixed number form of (3/2)x + 2/4 can be achieved by dividing the numerator (3) by the denominator (2).
3 ÷ 2 = 1 remainder 1
Therefore, the mixed number form is:
1 and 1/2x + 2/4
To simplify and add the fractions, follow these steps:
Step 1: Distribute the fractions by multiplying each fraction by the term outside 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
Step 2: Combine like terms by adding the coefficients of x:
1/2x + 1 + 1x - 1/2
Step 3: Combine the whole numbers by adding the constants:
1 + (-1/2) = 1/2
Step 4: Combine the x terms:
1/2x + 1x = 3/2x
The final answer in mixed number form is: 1/2 + 3/2x.