Simplify the Expression: 18x-7+4x-9-8x Step-by-Step

Combining Like Terms with Mixed Variables

18x7+4x98x=? 18x-7+4x-9-8x=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simplify the expression
00:05 Mark the appropriate variables
00:09 Use the commutative law and arrange the appropriate variables together
00:17 Collect like terms
00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

18x7+4x98x=? 18x-7+4x-9-8x=\text{?}

2

Step-by-step solution

To solve the exercise, we will reorder the numbers using the substitution property.

18x8x+4x79= 18x-8x+4x-7-9=

To continue, let's remember an important rule:

1. It is impossible to add or subtract numbers with variables.

That is, we cannot subtract 7 from 8X, for example...

We solve according to the order of arithmetic operations, from left to right:

18x8x=10x 18x-8x=10x 10x+4x=14x 10x+4x=14x 79=16 -7-9=-16 Remember, these two numbers cannot be added or subtracted, so the result is:

14x16 14x-16

3

Final Answer

14x16 14x-16

Key Points to Remember

Essential concepts to master this topic
  • Rule: Only combine terms with identical variables and powers
  • Technique: Group x-terms first: 18x - 8x + 4x = 14x
  • Check: Count variable terms (3) and constants (2) match original ✓

Common Mistakes

Avoid these frequent errors
  • Adding variables to constants
    Don't try to combine 18x - 7 = 11x! Variables and constants are completely different types that can't be combined. This creates impossible equations. Always separate x-terms from number terms and combine each group separately.

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

Why can't I subtract 7 from 18x?

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Think of variables like apples and constants like oranges - you can't add 18 apples minus 7 oranges! Variables represent unknown values, while constants are fixed numbers. They must stay separate.

What's the correct order to combine terms?

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First, rearrange to group like terms together: put all x-terms together and all constants together. Then combine within each group: 18x8x+4x 18x - 8x + 4x and 79 -7 - 9 .

How do I know which terms are like terms?

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Like terms have identical variables with the same powers. In this problem, 18x, 4x, and -8x are all like terms because they're all just 'x'. The numbers -7 and -9 are like terms because they're both constants.

What if I get confused with the negative signs?

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Remember that subtraction means adding the opposite. So 18x8x 18x - 8x becomes 18x+(8x)=10x 18x + (-8x) = 10x . Take your time with signs - they're the trickiest part!

Can I check my answer somehow?

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Yes! Pick any number for x (like x = 1) and substitute it into both the original expression and your simplified answer. If you get the same result from both, you're correct!

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