Simplify the Expression: 3z + 19z - 4z | Step-by-Step Solution

Q: What makes terms 'like terms' that can be combined?

Like terms have the exact same variable part! In $ 3z + 19z - 4z $, all terms have the variable z, so they can be combined by adding their coefficients.

Q: Do I add or multiply the numbers in front of the variables?

You add the coefficients (numbers in front)! Think of it like counting: 3 apples + 19 apples - 4 apples = 18 apples. Here: 3z + 19z - 4z = 18z.

Q: Why can't I just write 18 as my final answer?

Because the original expression has a variable z! When you combine like terms, you keep the variable part. $ 18z $ means 18 times whatever z equals, not just 18.

Q: What if some coefficients are negative?

Treat negative signs as part of the coefficient! In $ 3z + 19z - 4z $, the -4 means you're subtracting 4z, so: $ 3 + 19 - 4 = 18 $.

Q: How do I check if my answer is correct?

Pick any number for z and substitute it into both the original expression and your answer. If z = 2: $ 3(2) + 19(2) - 4(2) = 6 + 38 - 8 = 36 $ and $ 18(2) = 36 $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's simplify this expression step by step.

00:09 First, gather all similar terms together.

00:13 Now, let's calculate each operation one at a time. Take it slow and focus.

00:24 And there you have it! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$3z+19z-4z=\text{?}$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Combine like terms by identifying and adding their coefficients.
Step 2: Simplify the expression.
Step 3: Verify the resulting expression with the provided choices.

Let's work through each step:

Step 1: Identify the coefficients in the expression $3z + 19z - 4z$ . The coefficients are $3$ , $19$ , and $-4$ .

Step 2: Add and subtract these coefficients: $3 + 19 - 4$ .

Step 3: Calculate: $3 + 19 = 22$ and then $22 - 4 = 18$ .

Therefore, the simplified expression is $18z$ .

The solution to the problem is $18z$ .

3

Final Answer

$18z$

Key Points to Remember

Essential concepts to master this topic

Like Terms: Terms with same variable can be combined together
Technique: Add coefficients: $3 + 19 - 4 = 18$
Check: Verify by substituting: if $z = 1$ , then $3 + 19 - 4 = 18$ ✓

Common Mistakes

Avoid these frequent errors

Trying to combine unlike terms or forgetting the variable
Don't add $3z + 19z - 4z = 18$ without the variable! This loses the variable completely and gives a number instead of an expression. Always keep the variable when combining like terms: $18z$ .

Practice Quiz

Test your knowledge with interactive questions

Are the expressions the same or not?

$$ 20x $$

$2\times10x$

FAQ

Everything you need to know about this question

What makes terms 'like terms' that can be combined?

+

Like terms have the exact same variable part! In $3z + 19z - 4z$ , all terms have the variable z, so they can be combined by adding their coefficients.

Do I add or multiply the numbers in front of the variables?

+

You add the coefficients (numbers in front)! Think of it like counting: 3 apples + 19 apples - 4 apples = 18 apples. Here: 3z + 19z - 4z = 18z.

Why can't I just write 18 as my final answer?

+

Because the original expression has a variable z! When you combine like terms, you keep the variable part. $18z$ means 18 times whatever z equals, not just 18.

What if some coefficients are negative?

+

Treat negative signs as part of the coefficient! In $3z + 19z - 4z$ , the -4 means you're subtracting 4z, so: $3 + 19 - 4 = 18$ .

How do I check if my answer is correct?

+

Pick any number for z and substitute it into both the original expression and your answer. If z = 2: $3(2) + 19(2) - 4(2) = 6 + 38 - 8 = 36$ and $18(2) = 36$ ✓

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Simplify the Expression: 3z + 19z - 4z | Step-by-Step Solution

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