Simplify 4x + 8x using the properties of operations.(1 point)

Question

Simplify 4x + 8x using the properties of operations.(1 point)
Responses

12x2
12 x squared

4x + 8
4 x plus 8

12x
12 x

4 + 8x

GPT-4o mini · Answer

To simplify $4x + 8x$, you can combine like terms. Both terms have $x$ as a variable. So, $$ 4x + 8x = (4 + 8)x = 12x $$ The simplified expression is $12x$. Among the response options given, the correct one is: **12x** (12 x).

nope · Answer

Simplify 9g−7h−6g + 2h . (1 point) Responses 3g + 5h 3 g plus 5 h −2gh negative 2 g h 2gh − 4gh 2 g h minus 4 g h 3g − 5h

GPT-4o mini · Answer

To simplify $9g − 7h − 6g + 2h$, we can combine like terms. 1. Combine the $g$ terms: $$ 9g - 6g = (9 - 6)g = 3g $$ 2. Combine the $h$ terms: $$ -7h + 2h = (-7 + 2)h = -5h $$ Putting it all together, we have: $$ 3g - 5h $$ Among the response options given, the correct one is: **3g − 5h**.

nope · Answer

Simplify 2a − 4b +7 + 8a + 6b − 2.(1 point) Responses 12ab + 5 12 a b plus 5 −2ab + 14ab + 5 negative 2 a b plus 14 a b plus 5 10a − 2b +5 10 a minus 2 b plus 5 10a + 2b +5

GPT-4o mini · Answer

To simplify $2a − 4b + 7 + 8a + 6b − 2$, we can combine like terms step by step. 1. **Combine the $a$ terms:** $$ 2a + 8a = 10a $$ 2. **Combine the $b$ terms:** $$ -4b + 6b = 2b $$ 3. **Combine the constant terms:** $$ 7 - 2 = 5 $$ Putting it all together, we have: $$ 10a + 2b + 5 $$ Among the response options given, the correct one is: **10a + 2b + 5**.

nope · Answer

Simplify 3/7x + 2/7x using properties of operations.(1 point)
Responses

5/14x
Start Fraction 5 over 14 End Fraction x

5/14x2
Start Fraction 5 over 14 End Fraction x squared

5/7x2
Start Fraction 5 over 7 End Fraction x squared

5/7x

GPT-4o mini · Answer

To simplify $\frac{3}{7}x + \frac{2}{7}x$, you can combine the like terms since they both have $x$ as a common factor. 1. Combine the coefficients: $$ \frac{3}{7} + \frac{2}{7} = \frac{3 + 2}{7} = \frac{5}{7} $$ 2. Since both terms also include $x$, we can write: $$ \frac{5}{7}x $$ Among the response options given, the correct one is: **$\frac{5}{7}x$** (5/7x).

nope · Answer

Simplify 6/7c − 5/9d − 1/2 c + 1/3d.(1 point)
Responses

5/9c − 4/12d = 5/9c −1/3d
Start Fraction 5 over 9 End Fraction c minus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c minus Start Fraction 1 over 3 End Fraction d

5/14c − 2/9d
Start Fraction 5 over 14 End Fraction c minus Start Fraction 2 over 9 End Fraction d

5/9c + 4/12d = 5/9c +1/3d
Start Fraction 5 over 9 End Fraction c plus Start Fraction 4 over 12 End Fraction d equals Start Fraction 5 over 9 End Fraction c plus Start Fraction 1 over 3 End Fraction d

5/14c + 2/9d

GPT-4o mini · Answer

To simplify the expression $ \frac{6}{7}c - \frac{5}{9}d - \frac{1}{2}c + \frac{1}{3}d $, we need to combine like terms. First, let’s group the $c$ terms and the $d$ terms separately: 1. **For the $c$ terms**: - Combine $ \frac{6}{7}c $ and $ -\frac{1}{2}c $. - To do this, we need a common denominator. The least common denominator (LCD) for 7 and 2 is 14. Converting each term: $$ \frac{6}{7}c = \frac{12}{14}c \quad \text{(since } 6 \times 2 = 12\text{)} $$ $$ -\frac{1}{2}c = -\frac{7}{14}c \quad \text{(since } 1 \times 7 = 7\text{)} $$ Now combine: $$ \frac{12}{14}c - \frac{7}{14}c = \frac{12 - 7}{14}c = \frac{5}{14}c $$ 2. **For the $d$ terms**: - Combine $ -\frac{5}{9}d $ and $ \frac{1}{3}d $. - The least common denominator for 9 and 3 is 9. Converting: $$ \frac{1}{3}d = \frac{3}{9}d \quad \text{(since } 1 \times 3 = 3\text{)} $$ Now combine: $$ -\frac{5}{9}d + \frac{3}{9}d = \frac{-5 + 3}{9}d = -\frac{2}{9}d $$ Putting it all together, we have: $$ \frac{5}{14}c - \frac{2}{9}d $$ Among the response options given, the correct one is: **$\frac{5}{14}c - \frac{2}{9}d$** (5/14c − 2/9d).