Question

What value of Y would make the expression YB − 6 + 7 + 2B − 3B + 1 equivalent to 5B + 2?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression YB − 6 + 7 + 2B − 3B + 1, we can combine like terms:

YB + 2B − 3B + 7 + 1 − 6.

Combining the similar terms, we have:

(Y + 2 - 3)B + (7 + 1 - 6).

Simplifying further, we get:

(Y - 1)B + 2.

We want this expression to be equivalent to 5B + 2, so,

(Y - 1)B + 2 = 5B + 2.

Since the two expressions are equal, their coefficients must be the same:

Y - 1 = 5.

To find the value of Y, we add 1 to both sides:

Y = 5 + 1.

Therefore, the value of Y that makes the two expressions equivalent is Y = 6.

Answer 2

Generate an expression equivalent to: 4 ( h + 2 ) + 2 ( h + 1 ). The answer should be in simplest form.(1 point)

__h +__

Answer 3

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 4(h + 2) + 2(h + 1), we distribute the numbers outside the parentheses:

4 * h + 4 * 2 + 2 * h + 2 * 1

Simplifying further, we multiply:

4h + 8 + 2h + 2

Now, we add the like terms:

(4h + 2h) + (8 + 2)

Combine the similar terms:

6h + 10.

Therefore, an expression equivalent to 4(h + 2) + 2(h + 1) in simplest form is:

6h + 10.

Answer 4

Generate an expression equivalent to: 5+6b+12c+10b−4c−2 . In the simplest form of the equivalent expression, what is the coefficient of variable b ?(1 point

Answer 5

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 5 + 6b + 12c + 10b - 4c - 2, we can combine like terms:

(6b + 10b) + (12c - 4c) + (5 - 2)

Combine the similar terms:

16b + 8c + 3

Therefore, in the simplest form of the equivalent expression, the coefficient of the variable b is 16.

Answer 6

Use the properties of operations to write an expression equivalent to 2(k+4)+5 . The answer should be in simplest form. What is the constant value (no variables) in the equivalent expression?(1 point)

Answer 7

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 2(k + 4) + 5, we can distribute the number outside the parentheses:

2 * k + 2 * 4 + 5

Simplifying further, we multiply:

2k + 8 + 5

Now, we add the like terms:

2k + 13

Therefore, an expression equivalent to 2(k + 4) + 5 in simplest form is:

2k + 13.

In the equivalent expression, the constant value (no variables) is 13.

Answer 8

Apply the properties of operations to determine which expression is equivalent to a+b+c(d+2) .(1 point)

Responses

2abcd
2 a b c d

a+b+cd+2c
a plus b minus c d minus 2 c

a+b+cd+c
a plus b minus c d plus 2 c

a+b+cd+2

Answer 9

[AI-generated answer — Bot GPT 3.5]

The expression that is equivalent to a+b+c(d+2) is:

a+b+cd+2c.

Answer 10

Are the expressions 3+(4x+1) and 4−4x equivalent?(1 point)

Responses

No, they are not because 3+(4x+1) simplifies to 4+4x , which is not equivalent to 4−4x.
No, they are not because 3 minus left parenthesis 4 x plus 1 right parenthesis simplifies to 2 minus 4 x , which is not equivalent to 4 minus 4 x .

No, they are not because 3+(4x+1) simplifies to x+1, which is not equivalent to 4−4x.
No, they are not because 3 minus left parenthesis 4 x plus 1 right parenthesis simplifies to x plus 1 , which is not equivalent to 4 minus 4 x .

Yes, they are because both expressions simplify to 4−4x.
Yes, they are because both expressions simplify to 4 minus 4 x .

Yes, they are because both expressions simplify to 0.

Answer 11

[AI-generated answer — Bot GPT 3.5]

No, they are not because 3+(4x+1) simplifies to 4+4x, which is not equivalent to 4−4x.