how can i combine the like terms in this problem: 2z+4-3z=8z+19-4z+2
Combine like terms:
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.
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:
On the right side, the like terms are 8z and -4z. We also have 19 and 2. Combining each of these we get:
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