how can i combine the like terms in this problem: 2z+4-3z=8z+19-4z+2

Combine like terms:

2z+4-3z=8z+19-4z+2

What is a term? In this case, a term is a number, a variable, or a combination of numbers and variables which are being multiplied together.

For example,

4 is a term.

2z is also a term, because the 2 and the z are being multiplied.

In the equation you gave, the terms are separated from each other by + or – signs.

4 and 19 are both numbers without variables. They are like terms.

2z and -3z are like terms with variables.

4 and 2z are NOT like terms.

Let’s start with the left half of the equation.

The like terms on that side are 2z and -3z. Think of this as say, 2 zebras, minus 3 zebras. What you are left with is owing a zebra (-1z). (It doesn’t have to be zebras. The Z actually represents a number, but I sometimes find using a concrete object as a placeholder helps.)

So we get:

4-1z=8z+19-4z+2

On the right side, the like terms are 8z and -4z. We also have 19 and 2. Combining each of these we get:

4-1z=4z+21

The 8z and -4z combined to leave 4z. The 19 and 2 combined to leave 21.

If you need to solve for z, it is just a matter of isolating z on one side.

Add 1z to both sides:

4 = 5z +21

Subtract 21 from both sides:

-17 = 5z

Divide both sides by 5:

-17/5 = z