Question

consider the equation a(3-x)=-2x+b what values of a and b make x=-2

-9 -5 -1 5 9
a= b=

Answer 1

a(3-(-2))=-2(-2)+b

5a = 4+b
So now finish it off

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the values of a and b that make x = -2, we can substitute x = -2 into the equation:

a(3 - x) = -2x + b

Replacing x with -2, we get:

a(3 - (-2)) = -2(-2) + b

Simplifying further:

a(3 + 2) = 4 + b

a(5) = 4 + b

5a = 4 + b

Now, let's look at the given options for the value of a and b:

-9, -5, -1, 5, 9

We'll substitute each option and see which values satisfy the equation:

For a = -9:

5(-9) = 4 + b

-45 = 4 + b

b = -45 - 4

b = -49

For a = -5:

5(-5) = 4 + b

-25 = 4 + b

b = -25 - 4

b = -29

For a = -1:

5(-1) = 4 + b

-5 = 4 + b

b = -5 - 4

b = -9

For a = 5:

5(5) = 4 + b

25 = 4 + b

b = 25 - 4

b = 21

For a = 9:

5(9) = 4 + b

45 = 4 + b

b = 45 - 4

b = 41

So, the values of a and b that make x = -2 are:

a = -9, b = -49

a = -5, b = -29

a = -1, b = -9

a = 5, b = 21

a = 9, b = 41

Answer 3

[AI-generated answer — Explain Bot]

To find the values of a and b that make x = -2 in the equation a(3-x) = -2x + b, we can substitute the value x = -2 into the equation and solve for a and b.

Substituting x = -2 into the equation, we have:

a(3 - (-2)) = -2(-2) + b

Simplifying the equation:

a(3 + 2) = 4 + b

a(5) = 4 + b

Now we have the equation:

5a = 4 + b

Since we don't have any additional information or constraints, there can be multiple values of a and b that satisfy this equation. We can choose any arbitrary values for a, and then solve for the corresponding value of b.

Let's choose a = 1:

5(1) = 4 + b

5 = 4 + b

Subtracting 4 from both sides of the equation:

5 - 4 = b

1 = b

So, one possible solution is a = 1 and b = 1.

However, there can be other valid solutions as well. For example, if we choose a = 2, we'll get:

5(2) = 4 + b

10 = 4 + b

Subtracting 4 from both sides:

10 - 4 = b

6 = b

So, another possible solution is a = 2 and b = 6.

In summary, there can be multiple values of a and b that make x = -2 in the equation a(3-x) = -2x + b. Some possible solutions are a = 1 and b = 1, and a = 2 and b = 6.