Simplify the Expression: 17x + 3x + 11x Step-by-Step

Q: Why can I add 17x + 3x + 11x directly?

Because these are like terms - they all have the same variable x raised to the same power (1). When terms are alike, you can combine their coefficients: $ 17x + 3x + 11x = (17 + 3 + 11)x = 31x $

Q: What if the terms had different variables like 17x + 3y + 11x?

You can only combine terms with the same variable! So 17x + 3y + 11x becomes 28x + 3y because 17x and 11x are like terms, but 3y is different.

Q: Do I have to go left to right, or can I add in any order?

You can add in any order you want! Addition is commutative, so 17 + 3 + 11 = 17 + 11 + 3 = 31. Choose whatever order feels easiest for you.

Q: How do I know when terms are 'like terms'?

Terms are like terms when they have:Same variable(s) (both have x)Same exponent (both x to the first power)Examples: 5x and 12x are like terms, but 5x and 5x² are not!

Q: What if one term was just x without a number?

Remember that x means 1x! So if you had 17x + x + 11x, it would be 17x + 1x + 11x = 29x. The invisible coefficient is always 1.

Like Terms with Multiple Variable Coefficients

$17x+3x+11x=$ ?

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Step-by-step video solution

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00:00 Solve

00:03 Let's solve according to order of operations, from left to right

00:06 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$17x+3x+11x=$ ?

Step-by-step solution

Since we only have numbers in the exercise that are coefficients of x, we can solve the exercise from left to right:

$17x+3x=20x$

$20x+11x=31x$

Final Answer

$31x$

Key Points to Remember

Essential concepts to master this topic

Rule: Add coefficients of like terms with same variable
Technique: Combine left to right: 17x + 3x = 20x, then 20x + 11x = 31x
Check: Factor out x: x(17 + 3 + 11) = x(31) = 31x ✓

Common Mistakes

Avoid these frequent errors

Adding the variable x to the coefficient sum
Don't write 17 + 3 + 11 + x = 31 + x! This treats x as a number to add instead of the common variable factor. Always add only the coefficients and keep the variable unchanged: 17x + 3x + 11x = 31x.

Practice Quiz

Test your knowledge with interactive questions

$$ 94+12+6= $$

FAQ

Everything you need to know about this question

Why can I add 17x + 3x + 11x directly?

Because these are like terms - they all have the same variable x raised to the same power (1). When terms are alike, you can combine their coefficients: $17x + 3x + 11x = (17 + 3 + 11)x = 31x$

What if the terms had different variables like 17x + 3y + 11x?

You can only combine terms with the same variable! So 17x + 3y + 11x becomes 28x + 3y because 17x and 11x are like terms, but 3y is different.

Do I have to go left to right, or can I add in any order?

You can add in any order you want! Addition is commutative, so 17 + 3 + 11 = 17 + 11 + 3 = 31. Choose whatever order feels easiest for you.

How do I know when terms are 'like terms'?

Terms are like terms when they have:

Same variable(s) (both have x)
Same exponent (both x to the first power)

Examples: 5x and 12x are like terms, but 5x and 5x² are not!

What if one term was just x without a number?

Remember that x means 1x! So if you had 17x + x + 11x, it would be 17x + 1x + 11x = 29x. The invisible coefficient is always 1.

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