Solve the Linear Equation: 20+20x-3x=88

Q: Why do I need to combine like terms first?

Combining like terms simplifies your equation and makes it easier to solve! Instead of working with $ 20x - 3x $ separately, you get the cleaner $ 17x $.

Q: What are like terms exactly?

Like terms have the same variable with the same exponent. In this problem, $ 20x $ and $ -3x $ are like terms because they both have x to the first power.

Q: Can I subtract 20 from both sides first instead?

You could, but it's much harder! You'd get $ 20x - 3x = 68 $ and still need to combine like terms anyway. Always simplify first for easier calculations.

Q: How do I know which terms to combine?

Look for terms with the exact same variable part. Here, both $ 20x $ and $ 3x $ have just 'x', so they combine to $ (20-3)x = 17x $.

Q: What if I get a different answer when checking?

If substituting doesn't work, go back and check your arithmetic! Common errors include sign mistakes when combining terms or calculation errors when dividing.

Linear Equations with Like Term Combining

$20+20x-3x=88$

$x=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:07 Let's arrange the equation so that one side has only the unknown X

00:13 Let's group terms

00:19 Let's isolate the unknown X

00:28 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

$20+20x-3x=88$

$x=\text{?}$

Step-by-step solution

To solve this problem, we need to find $x$ in the equation:

$20 + 20x - 3x = 88$

Step 1: Combine like terms on the left-hand side of the equation. The terms involving $x$ are $20x$ and $-3x$ .

$20x - 3x = 17x$

Thus, the equation becomes:

$20 + 17x = 88$

Step 2: Isolate the $x$ -related terms by moving the constant term to the right-hand side. To do this, subtract 20 from both sides:

$17x = 88 - 20$

$17x = 68$

Step 3: Solve for $x$ by dividing both sides of the equation by 17:

$x = \frac{68}{17}$

$x = 4$

Therefore, the solution to the problem is $x = 4$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Rule: Combine like terms first before isolating the variable
Technique: Simplify $20x - 3x = 17x$ to get cleaner equation
Check: Substitute x = 4: 20 + 20(4) - 3(4) = 20 + 80 - 12 = 88 ✓

Common Mistakes

Avoid these frequent errors

Moving terms before combining like terms
Don't try to isolate x before combining 20x - 3x = wrong approach leads to messy fractions! This creates unnecessary complexity and calculation errors. Always combine like terms first to simplify the equation structure.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I need to combine like terms first?

Combining like terms simplifies your equation and makes it easier to solve! Instead of working with $20x - 3x$ separately, you get the cleaner $17x$ .

What are like terms exactly?

Like terms have the same variable with the same exponent. In this problem, $20x$ and $-3x$ are like terms because they both have x to the first power.

Can I subtract 20 from both sides first instead?

You could, but it's much harder! You'd get $20x - 3x = 68$ and still need to combine like terms anyway. Always simplify first for easier calculations.

How do I know which terms to combine?

Look for terms with the exact same variable part. Here, both $20x$ and $3x$ have just 'x', so they combine to $(20-3)x = 17x$ .

What if I get a different answer when checking?

If substituting doesn't work, go back and check your arithmetic! Common errors include sign mistakes when combining terms or calculation errors when dividing.

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