Solve the Linear Equation: Finding X in 5x-8=10x+22

Linear Equations with Variable Terms Both Sides

Solve for X:

5x8=10x+22 5x-8=10x+22

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 We want to isolate the unknown X
00:22 Let's reduce what we can
00:28 Let's group terms
00:35 Continue to isolate the unknown X
00:54 Group terms, and continue to isolate the unknown X
01:16 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

Solve for X:

5x8=10x+22 5x-8=10x+22

2

Step-by-step solution

First, we arrange the two sections so that the right side contains the values with the coefficient x and the left side the numbers without the x

Let's remember to maintain the plus and minus signs accordingly when we move terms between the sections.

First, we move a5x 5x to the right section and then the 22 to the left side. We obtain the following equation:

822=10x5x -8-22=10x-5x

We subtract both sides accordingly and obtain the following equation:

30=5x -30=5x

We divide both sections by 5 and obtain:

6=x -6=x

3

Final Answer

6 -6

Key Points to Remember

Essential concepts to master this topic
  • Collection Rule: Move all x-terms to one side, constants to other
  • Technique: Subtract 5x from both sides: 10x - 5x = 5x
  • Check: Substitute x = -6: 5(-6) - 8 = -38, 10(-6) + 22 = -38 ✓

Common Mistakes

Avoid these frequent errors
  • Moving terms without changing signs
    Don't move 5x to the right side as +5x when it starts as +5x on the left = wrong equation! This creates 15x instead of 5x and gives completely wrong answers. Always change the sign when moving terms across the equals sign.

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

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

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Moving all x terms to one side lets you combine like terms and solve for x directly. If you leave x terms on both sides, you can't isolate x to find its value.

Which side should I move the x terms to?

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Move them to whichever side gives you a positive coefficient for x. In this problem, moving to the right gives 5x (positive), which is easier than -5x.

Do I always change the sign when moving terms?

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Yes, always! When you move a term across the equals sign, you're really adding or subtracting it from both sides. +5x becomes -5x when moved.

What if I get a negative answer for x?

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Negative solutions are completely normal! Many equations have negative answers. Just make sure to check your work by substituting back into the original equation.

Can I move the constants first instead of the x terms?

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Yes! You can move terms in any order you prefer. Some students find it easier to move constants first, then x terms. The final answer will be the same.

How do I avoid making sign errors?

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Write each step clearly and double-check signs before moving to the next step. Remember: moving left to right changes + to - and - to +.

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