Help?Simplify each expression.1. 3w – 10w a. 13w
b. –7w c. –7 d. 7w 2. y + 1.2y +1.2z a. 2.4yz b. 1.3y + 1.2z c. 1.2y2 + 1.2z
d. 2.2y + 1.2z 3. 6r + r – 5r a. 2r b. 1r + r c. 0r d. 7r – 5r
4. 5x + 2(x + 6) a. 7x + 6 b. 7x2 + 12 c. 7x + 12 d. 7x (x + 6)
5. –3m + 3(m + 6) a. 6 b. –6m + 6 c. 6m + 18 d. 18
3w-10w = (3-10)w = -7w
do the others in like wise.
Sure! I can help you with that. Let's simplify each expression step-by-step:
1. 3w - 10w:
- Combine like terms. Since both terms have the variable w, we can subtract the coefficients:
- 3w - 10w = -7w
Therefore, the simplified expression is b. -7w
2. y + 1.2y + 1.2z:
- Combine like terms. Since both terms have the variable y, we can add the coefficients:
- y + 1.2y = 2.2y
The z term remains the same.
Therefore, the simplified expression is d. 2.2y + 1.2z
3. 6r + r - 5r:
- Combine like terms. The first two terms have the variable r, so we can add the coefficients and then subtract the third term:
- 6r + r - 5r = (6 + 1 - 5)r = 2r
Therefore, the simplified expression is a. 2r
4. 5x + 2(x + 6):
- Apply the distributive property by multiplying 2 to both terms inside the parentheses:
- 5x + 2(x + 6) = 5x + 2x + 12
- Combine like terms:
- 5x + 2x = 7x
The constant term remains the same.
Therefore, the simplified expression is c. 7x + 12
5. -3m + 3(m + 6):
- Apply the distributive property by multiplying 3 to both terms inside the parentheses:
- (-3m) + 3(m + 6) = -3m + 3m + 18
- Combine like terms:
- -3m + 3m = 0m (which simplifies to 0)
The constant term remains the same.
Therefore, the simplified expression is d. 18
I hope this helps! Let me know if you have any other questions.
1. To simplify the expression 3w - 10w, you can combine the like terms. Like terms are terms that have the same variable raised to the same power. In this case, both terms have the variable "w" raised to the power of 1.
To combine like terms, subtract the coefficients (numbers in front of the variables) and keep the common variable. In this case, we have 3w - 10w. Subtracting 10w from 3w gives us -7w. So the simplified expression is -7w. Therefore, the correct answer is option b. -7w.
2. To simplify the expression y + 1.2y + 1.2z, you can also combine the like terms. The variable "y" is raised to the power of 1 and appears in both terms, so we can add them together.
Adding the coefficients of the "y" terms, we get 1y + 1.2y = 2.2y. The "z" term does not have any other like terms, so it remains the same. Therefore, the simplified expression is 2.2y + 1.2z. So the correct answer is option d. 2.2y + 1.2z.
3. In the expression 6r + r - 5r, we have three terms with the variable "r". Two of the terms (6r and -5r) have the same variable raised to the power of 1 and are like terms.
Combining the coefficients of these like terms, we have 6r - 5r = 1r. However, we usually do not write the coefficient of 1, so the simplified expression is just "r". Therefore, the correct answer is option c. 0r.
4. In the expression 5x + 2(x + 6), we need to apply the distributive property to simplify it. The distributive property states that you need to multiply the term outside the parentheses (2) by each term inside the parentheses (x and 6).
Expanding the expression using the distributive property, we get 5x + 2x + 12. Now, we can combine the like terms. Adding the coefficients of the "x" terms, we have 5x + 2x = 7x. The constant term of 12 does not have any other like terms, so it remains the same.
Therefore, the simplified expression is 7x + 12. So the correct answer is option c. 7x + 12.
5. In the expression -3m + 3(m + 6), we again need to apply the distributive property. The -3m term does not have any like terms, so it remains the same.
Expanding the expression using the distributive property, we get -3m + 3m + 18. Now, we can combine the like terms. Adding the coefficients of the "m" terms, we have -3m + 3m = 0m (which is why option c. 0r is not correct in this case).
The constant term of 18 does not have any other like terms, so it remains the same. Therefore, the simplified expression is 0m + 18, which can be written as just 18. So the correct answer is option d. 18.