Asked by Clueless
add: 1/2(x+4)+1/4(4x-2). Answer should be in mixed number form.(1 point)
Answers
Answered by
GPT 3.5
To simplify the expression, we can first distribute the fractions:
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
= (1/2)x + 1 + x - 1/2.
We can now combine like terms:
= (1/2)x + x + 1 - 1/2
= (3/2)x + 1 - 1/2.
To add the mixed number, we first need to find a common denominator for the fractions.
The common denominator for 2 and 1 is 2.
The common denominator for 2 and 1/2 is 2.
Now we can add the fractions:
= (3/2)x + (2/2) - (1/2)
= (3/2)x + (1/2).
Therefore, the simplified expression is (3/2)x + (1/2).
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
= (1/2)x + 1 + x - 1/2.
We can now combine like terms:
= (1/2)x + x + 1 - 1/2
= (3/2)x + 1 - 1/2.
To add the mixed number, we first need to find a common denominator for the fractions.
The common denominator for 2 and 1 is 2.
The common denominator for 2 and 1/2 is 2.
Now we can add the fractions:
= (3/2)x + (2/2) - (1/2)
= (3/2)x + (1/2).
Therefore, the simplified expression is (3/2)x + (1/2).
Answered by
GPT 3.5
To simplify the expression, we can first distribute the fractions:
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
= (1/2)x + 1 + x - 1/2
= (3/2)x + 1 - 1/2
Next, we can add the whole numbers and fractions separately:
= (3/2)x + (1/2)
Since the coefficient in front of the variable, (3/2), is greater than 1, we can convert it to a mixed number.
To convert (3/2) to a mixed number, we divide the numerator (3) by the denominator (2). The quotient is the whole number, and the remainder is the numerator of the fraction:
3 ÷ 2 = 1 remainder 1
So, the mixed number form of (3/2) is 1 and 1/2.
Therefore, the simplified expression in mixed number form is:
1 and 1/2x + 1/2.
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
= (1/2)x + 1 + x - 1/2
= (3/2)x + 1 - 1/2
Next, we can add the whole numbers and fractions separately:
= (3/2)x + (1/2)
Since the coefficient in front of the variable, (3/2), is greater than 1, we can convert it to a mixed number.
To convert (3/2) to a mixed number, we divide the numerator (3) by the denominator (2). The quotient is the whole number, and the remainder is the numerator of the fraction:
3 ÷ 2 = 1 remainder 1
So, the mixed number form of (3/2) is 1 and 1/2.
Therefore, the simplified expression in mixed number form is:
1 and 1/2x + 1/2.
Answered by
GPT 3.5
Apologies for the mistake. Let's go through the simplification again.
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
= (1/2)x + 1 + x - 1/2
= (3/2)x + 1 - 1/2
Next, let's rewrite 1 as a fraction with a common denominator of 2:
= (3/2)x + 2/2 - 1/2
= (3/2)x + 2/2 - 1/2
Now, we can add the fractions:
= (3/2)x + 2/2 - 1/2
= (3/2)x + 1/2
Therefore, the simplified expression in mixed number form is:
1 and 1/2x.
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
= (1/2)x + 1 + x - 1/2
= (3/2)x + 1 - 1/2
Next, let's rewrite 1 as a fraction with a common denominator of 2:
= (3/2)x + 2/2 - 1/2
= (3/2)x + 2/2 - 1/2
Now, we can add the fractions:
= (3/2)x + 2/2 - 1/2
= (3/2)x + 1/2
Therefore, the simplified expression in mixed number form is:
1 and 1/2x.
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