Simplify 8a − 2a.
Simplify 12e − 5f − 7e +3f.
Simplify 9x + 3y − 6 − 5x + 4y −3.
Simplify 9/11z − 4/11z.
Simplify 3/10x + 1/6y + 3/10x + 3/6y. Be sure to reduce any fractions to the lowest terms.
A1. 6a
A2. 5e - 2f
A3. 4x + 7y - 9
A4. 5/11z
A5. 3/5x + 2/3y
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8a - 2a = 6a
12e - 5f - 7e + 3f = (12e - 7e) + (-5f + 3f) = 5e - 2f
9x + 3y - 6 - 5x + 4y - 3 = (9x - 5x) + (3y + 4y) + (-6 - 3) = 4x + 7y - 9
9/11z - 4/11z = (9z - 4z)/11 = 5z/11
3/10x + 1/6y + 3/10x + 3/6y = (3/10x + 3/10x) + (1/6y + 3/6y) = 6/10x + 4/6y = 3/5x + 2/3y
simplify 12e - 5f - 7e + 3f
To simplify these expressions, we'll combine like terms by adding or subtracting them.
1. 8a - 2a:
Step 1: Combine the like terms 8a and -2a.
8a - 2a = (8 - 2)a = 6a
2. 12e - 5f - 7e +3f:
Step 1: Group the like terms together.
(12e - 7e) + (-5f + 3f)
Step 2: Combine the like terms within each group.
5e - 2f
3. 9x + 3y - 6 - 5x + 4y -3:
Step 1: Group the like terms together.
(9x - 5x) + (3y + 4y) + (-6 - 3)
Step 2: Combine the like terms within each group and simplify.
4x + 7y - 9
4. 9/11z - 4/11z:
Step 1: Combine the like terms.
9/11z - 4/11z = (9/11 - 4/11)z = 5/11z
5. 3/10x + 1/6y + 3/10x + 3/6y:
Step 1: Group the like terms together.
(3/10x + 3/10x) + (1/6y + 3/6y)
Step 2: Combine the like terms within each group.
6/10x + 4/6y
Step 3: Simplify the fractions, if possible.
3/5x + 2/3y
To simplify expressions involving multiple terms and coefficients, we can combine like terms. Like terms are terms that have the same variables raised to the same powers.
Let's go through each expression one by one:
1. Simplify 8a - 2a
To simplify this expression, we combine the terms with the same variable, which in this case is 'a':
8a - 2a = (8 - 2)a = 6a
2. Simplify 12e - 5f - 7e + 3f
Here, we combine the like terms 'e' and 'f':
12e - 7e - 5f + 3f = (12 - 7)e + (-5 + 3)f = 5e - 2f
3. Simplify 9x + 3y - 6 - 5x + 4y - 3
First, combine the 'x' terms and 'y' terms:
9x - 5x + 3y + 4y = (9 - 5)x + (3 + 4)y = 4x + 7y
Finally, combine the constants:
4x + 7y - 6 - 3 = 4x + 7y - 9
4. Simplify 9/11z - 4/11z
Here, we have the same variable 'z' and the same denominator, so we can simply subtract the coefficients:
9/11z - 4/11z = (9/11 - 4/11)z = 5/11z
5. Simplify 3/10x + 1/6y + 3/10x + 3/6y
First, combine the 'x' terms and 'y' terms:
3/10x + 3/10x + 1/6y + 3/6y = (3/10 + 3/10)x + (1/6 + 3/6)y = 6/10x + 4/6y = 3/5x + 2/3y
Since the fractions have different denominators, we need to find a common denominator before adding or subtracting them. The least common multiple (LCM) of 5 and 3 is 15. Multiply the numerators and denominators by appropriate values to get the common denominator:
(3/5)*(3/3)x + (2/3)*(5/5)y = 9/15x + 10/15y
Finally, reducing the fractions, we get:
9/15x + 10/15y = 3/5x + 2/3y