1. rebecca was asked to create five pairs of like terms. determine if she completed the task correctly and correct any errors.
2.5w and -8w
$\frac{1}{2}x$ and $\frac{1}{2}$
38 and -15
-7c² and c²
5a and 5b

in questions 2-10, simplify the expressions by combining like terms.

2. $4r + 9r - 11r + 7r$
3. $-r + 6 + 8r - 14$
4. $-26r + 7r - 15p - 7p$
5. $8r + 12p - 7 - 3p$
6. $10r - 5r + 3r - 8r$
7. $-4p - 2r - 15p$
8. $\frac{3}{4}r + 2r + \frac{1}{2}r$
9. $1.5r - 3r + 8r + 2.5r$
10. $\frac{2}{3}p + \frac{4}{3}p - \frac{1}{3}p$

11. simplify an expression for the perimeter of the rectangle.
diagram of rectangle with height (5w - 2) and width (3w)
perimeter: _______

Question

1. rebecca was asked to create five pairs of like terms. determine if she completed the task correctly and correct any errors.
2.5w and -8w
$\frac{1}{2}x$ and $\frac{1}{2}$
38 and -15
-7c² and c²
5a and 5b

in questions 2-10, simplify the expressions by combining like terms.

2. $4r + 9r - 11r + 7r$
3. $-r + 6 + 8r - 14$
4. $-26r + 7r - 15p - 7p$
5. $8r + 12p - 7 - 3p$
6. $10r - 5r + 3r - 8r$
7. $-4p - 2r - 15p$
8. $\frac{3}{4}r + 2r + \frac{1}{2}r$
9. $1.5r - 3r + 8r + 2.5r$
10. $\frac{2}{3}p + \frac{4}{3}p - \frac{1}{3}p$

11. simplify an expression for the perimeter of the rectangle.
diagram of rectangle with height (5w - 2) and width (3w)
perimeter: _______

Accepted Answer

### Question 1: Determine if Rebecca completed the task correctly and correct any errors.

#### Explanation:
Like terms are terms with the same variable (or no variable for constants) raised to the same power.
- **2.5w and -8w**: Both have variable $ w $, so like terms (correct).
- **$\frac{1}{2}x$ and $\frac{1}{2}$**: One has variable $ x $, the other is a constant—**not** like terms (error). Correct: e.g., $\frac{1}{2}x$ and $\frac{3}{2}x$, or $\frac{1}{2}$ and $ 5 $.
- **38 and -15**: Both constants, so like terms (correct).
- **$-7c^2$ and $ c^2 $**: Both have $ c^2 $, so like terms (correct).
- **5a and 5b**: Different variables ($ a $ vs. $ b $)—**not** like terms (error). Correct: e.g., 5a and 3a, or 5b and -2b.

#### Answer:
Rebecca made errors in the pairs $\boldsymbol{\frac{1}{2}x}$ and $\boldsymbol{\frac{1}{2}}$ (not like terms, as one has $ x $, the other is a constant) and $\boldsymbol{5a}$ and $\boldsymbol{5b}$ (not like terms, different variables). Correct pairs could be $\frac{1}{2}x$ and $\frac{3}{2}x$ (or other $ x $-terms) for the second, and $ 5a $ and $ 3a $ (or other $ a $-terms) for the fifth. The first, third, and fourth pairs are correct.

### Question 2: Simplify $ 4r + 9r - 11r + 7r $

#### Explanation:
Combine like terms (all have $ r $) by adding/subtracting coefficients.
- Step 1: Add coefficients: $ 4 + 9 - 11 + 7 $.
- Step 2: Calculate: $ 4 + 9 = 13 $; $ 13 - 11 = 2 $; $ 2 + 7 = 9 $.

#### Answer:
$ 9r $

### Question 3: Simplify $ -r + 6 + 8r - 14 $

#### Explanation:
Combine like terms: $ r $-terms and constants.
- Step 1: Combine $ r $-terms: $ -r + 8r = 7r $.
- Step 2: Combine constants: $ 6 - 14 = -8 $.

#### Answer:
$ 7r - 8 $

### Question 4: Simplify $ -26r + 7r - 15p - 7p $

#### Explanation:
Combine $ r $-terms and $ p $-terms separately.
- Step 1: $ r $-terms: $ -26r + 7r = -19r $.
- Step 2: $ p $-terms: $ -15p - 7p = -22p $.

#### Answer:
$ -19r - 22p $

### Question 5: Simplify $ 8r + 12p - 7 - 3p $

#### Explanation:
Combine $ p $-terms; $ r $ and constant remain.
- Step 1: $ p $-terms: $ 12p - 3p = 9p $.
- Step 2: Combine with $ 8r $ and $ -7 $.

#### Answer:
$ 8r + 9p - 7 $

### Question 6: Simplify $ 10r - 5r + 3r - 8r $

#### Explanation:
Combine all $ r $-terms by adding/subtracting coefficients.
- Step 1: Coefficients: $ 10 - 5 + 3 - 8 $.
- Step 2: Calculate: $ 10 - 5 = 5 $; $ 5 + 3 = 8 $; $ 8 - 8 = 0 $.

#### Answer:
$ 0 $ (or $ 0r $, but $ 0 $ is simpler)

### Question 7: Simplify $ -4p - 2r - 15p $

#### Explanation:
Combine $ p $-terms; $ r $ remains.
- Step 1: $ p $-terms: $ -4p - 15p = -19p $.
- Step 2: Combine with $ -2r $.

#### Answer:
$ -19p - 2r $

### Question 8: Simplify $ \frac{3}{4}r + 2r + \frac{1}{2}r $

#### Explanation:
Convert to common denominator (4) to add coefficients.
- Step 1: $ 2r = \frac{8}{4}r $, $ \frac{1}{2}r = \frac{2}{4}r $.
- Step 2: Add coefficients: $ \frac{3}{4} + \frac{8}{4} + \frac{2}{4} = \frac{13}{4} $.

#### Answer:
$ \frac{13}{4}r $ (or $ 3.25r $)

### Question 9: Simplify $ 1.5r - 3r + 8r + 2.5r $

#### Explanation:
Combine all $ r $-terms by adding/subtracting coefficients.
- Step 1: Coefficients: $ 1.5 - 3 + 8 + 2.5 $.
- Step 2: Calculate: $ 1.5 + 2.5 = 4 $; $ -3 + 8 = 5 $; $ 4 + 5 = 9 $.

#### Answer:
$ 9r $

### Question 10: Simplify $ \frac{2}{3}p + \frac{4}{3}p - \frac{1}{3}p $

#### Explanation:
Combine $ p $-terms (same denominator, so add/subtract numerators).
- Step 1: Numerators: $ 2 + 4 - 1 = 5 $.
- Step 2: Result: $ \frac{5}{3}p $.

#### Answer:
$ \frac{5}{3}p $ (or $ 1\frac{2}{3}p $)

### Question 11: Simplify the perimeter of the rectangle

#### Explanation:
Perimeter of a rectangle: $ P = 2(\text{length} + \text{width}) $. Length = $ 5w - 2 $, Width = $ 3w $.
- Step 1: Substitute into formula: $ P = 2[(5w - 2) + 3w] $.
- Step 2: Combine like terms inside: $ 5w + 3w - 2 = 8w - 2 $.
- Step 3: Multiply by 2: $ 2(8w - 2) = 16w - 4 $.

#### Answer:
$ 16w - 4 $

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QUESTION IMAGE

Question

Explanation:

Question 1: Determine if Rebecca completed the task correctly and correct any errors.

Answer:

Question 2: Simplify \( 4r + 9r - 11r + 7r \)