Please explain how to get the answer.

At the animal shelter, 1/3 of the animals are dogs, 2/12 are cats, and 19 are other animals. How many animals are at the shelter?

I said 1/3x + 2/12x + 19 =
4/12x + 2/12x = 19=
6/12x = 19
1/2x = 19
x =

Your first equation is incomplete, but if you make the final step, your answer will be correct.

1/3x + 2/12x + 19 = x OR

19 = x - 1/3x - 2/12x

19 = x - 2/6x - 1/6x

19 = x - 1/2x = 1/2x

38 = x

How does a 4th grader draw a picture to support this answer?

To find the total number of animals at the shelter, you'll need to solve for the variable x in the equation:

1/3x + 2/12x + 19 = x

Step 1: Simplify the fractions on the left side of the equation.

The fraction 2/12 can be reduced to 1/6 by dividing both the numerator and denominator by the greatest common divisor, which is 2.

The equation becomes:

1/3x + 1/6x + 19 = x

Step 2: Combine like terms on the left side of the equation.

The fractions 1/3x and 1/6x have the same denominator of 6x, so they can be added together.

The equation becomes:

2/6x + 1/6x + 19 = x

Simplifying the fractions gives:

3/6x + 19 = x

Step 3: Get rid of the fractions by multiplying both sides of the equation by 6, which is the least common multiple of 6 and x.

6 * (3/6x + 19) = 6 * x

This simplifies to:

3x + 114 = 6x

Step 4: Isolate the variable x by moving all terms containing x to one side of the equation.

Subtract 3x from both sides of the equation:

3x + 114 - 3x = 6x - 3x

This simplifies to:

114 = 3x

Step 5: Solve for x by dividing both sides of the equation by 3.

114 / 3 = 3x / 3

This simplifies to:

38 = x

So, the variable x represents the total number of animals at the shelter, and in this case, it is equal to 38. Therefore, there are 38 animals at the shelter.