Find X: Solving the Linear Equation 5 - 3x = 8x - 17

Q: Why do I need to move all the x terms to one side?

Moving all x terms to one side lets you combine them into a single coefficient. This makes it much easier to solve for x by dividing once at the end!

Q: Should I move x terms to the left or right side?

Either side works! Choose the side that gives you a positive coefficient for x. In this problem, moving to the right gives $ 11x $ instead of $ -11x $.

Q: What if I get a negative answer for x?

Negative solutions are completely normal! Always check your work by substituting back into the original equation to make sure both sides are equal.

Q: How do I avoid making arithmetic mistakes?

Write each step clearly on a new lineDouble-check your addition and subtractionAlways verify by substituting your answer back

Linear Equations with Variable Terms

Solve for X:

$5-3x=8x-17$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Arrange the equation so that one side has only the unknown X

00:22 Collect like terms

00:30 Isolate X

00:40 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$5-3x=8x-17$

Step-by-step solution

To solve this linear equation, follow these steps:

Step 1: Move all terms involving $x$ to one side of the equation.
Step 2: Move constant terms to the opposite side.
Step 3: Simplify the equation to isolate $x$ .
Step 4: Solve for $x$ by dividing by its coefficient.

Let's work through it:

Start with the given equation:
$5 - 3x = 8x - 17$

Step 1: Add $3x$ to both sides to move all $x$ terms to the right side:
$5 = 11x - 17$

Step 2: Add $17$ to both sides to move the constants to the left side:
$22 = 11x$

Step 3 & 4: Divide both sides by $11$ to isolate $x$ :
$x = \frac{22}{11}$

Simplifying the fraction gives:
$x = 2$

Hence, the solution to the problem is $x = 2$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Move all x terms to one side and constants to the other
Technique: Add 3x to both sides: 5 = 8x + 3x - 17
Check: Substitute x = 2: 5 - 3(2) = 8(2) - 17 gives -1 = -1 ✓

Common Mistakes

Avoid these frequent errors

Moving terms without changing signs
Don't move -3x to the right as -3x = wrong equation! When moving terms across the equals sign, you must change their signs. Always add 3x to both sides or subtract 3x from both sides.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why do I need to move all the x terms to one side?

Moving all x terms to one side lets you combine them into a single coefficient. This makes it much easier to solve for x by dividing once at the end!

Should I move x terms to the left or right side?

Either side works! Choose the side that gives you a positive coefficient for x. In this problem, moving to the right gives $11x$ instead of $-11x$ .

What if I get a negative answer for x?

Negative solutions are completely normal! Always check your work by substituting back into the original equation to make sure both sides are equal.

Can I solve this equation in a different order?

Yes! You could move constants first, then variables. The key is to do the same operation to both sides at each step to keep the equation balanced.

How do I avoid making arithmetic mistakes?

Write each step clearly on a new line
Double-check your addition and subtraction
Always verify by substituting your answer back

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