Add: (2m - 3) + (3n - 1) + (3m +1)
Combining like terms, we have:
(2m - 3) + (3n - 1) + (3m + 1)
= 2m + 3n - 3 - 1 + 3m + 1
= (2m + 3m) + 3n + (-3 - 1 + 1)
= 5m + 3n - 3.
Subtract: 2 (10b + 4) - (b -2)
Expanding the parentheses and distributing the negative sign, we have:
2(10b + 4) - (b - 2)
= 20b + 8 - b + 2
= 20b - b + 8 + 2
= 19b + 10.
(3g - 4) - 2 (3g + 4)
Expanding the parentheses and distributing the negative sign inside the second set of parentheses, we have:
(3g - 4) - 2(3g + 4)
= 3g - 4 - (2 * 3g + 2 * 4)
= 3g - 4 - (6g + 8)
= 3g - 4 - 6g - 8
= (3g - 6g) + (-4 - 8)
= -3g - 12.
Add: 1/2 (x + 4) + 1/4 (4x - 2) *put the answer in mixed number form*
To add the expressions, we can distribute the fractions and then combine like 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 - 1/2
= 1/2 * x + 1 + x - 1/2
= (1/2 * 2x + x) + (1 - 1/2)
= x + x + 1 - 1/2
= 2x + 1/2.
Thus, the answer is 2x + 1/2 in mixed number form.
wrong!
Apologies for the mistake. Let's go through the problem again.
1/2 (x + 4) + 1/4 (4x - 2)
First, distribute the fractions:
1/2 * x + 1/2 * 4 + 1/4 * 4x - 1/4 * 2
Simplify each term:
1/2 * x + 2 + 1x - 1/2
Consolidate the x-terms and the constant terms:
(1/2 * x + 1x) + (2 - 1/2)
Combining like terms:
(1/2x + 2x) + (4/2 - 1/2)
Simplify further:
(3/2x) + (3/2)
To add fractions, we need the same denominator:
(3/2x) + (3/2)
Since 2x does not have a common denominator of 2, we multiply both its numerator and denominator by 2 to obtain the common denominator:
(3/2x) + (3/2)
Now, the expression becomes:
(3/2x) + (3/2)
To add these fractions, we need the same denominator:
(3/2x) + (3/2)
The common denominator is 2x. Multiplying the numerators and denominators accordingly, we get:
(3 * x + 3 * 1) / (2 * x)
Simplifying the numerator and denominator:
(3x + 3) / (2x)
Therefore, the answer is (3x + 3) / (2x) in fractional form.
To simplify the given expression, we need to combine like terms. Like terms are terms that have the same variables raised to the same powers. Let's break down the expression step by step:
Step 1: Group the terms with the same variables together.
(2m - 3) + (3n - 1) + (3m + 1)
Step 2: Combine like terms within each group.
For the terms with variable 'm':
2m + 3m = (2 + 3)m = 5m
For the terms with variable 'n':
3n
For the terms without variables:
-3 - 1 + 1 = -3
Step 3: Combine the simplified terms from Step 2.
5m + 3n - 3
Therefore, the simplified expression is 5m + 3n - 3.