Solve Linear Equation: 74-6x+3=8x+5x-18 for Parameter X

Linear Equations with Multi-Term Simplification

Find the value of the parameter X

746x+3=8x+5x18 74-6x+3=8x+5x-18

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find X
00:04 Collect like terms
00:16 Arrange the equation so that one side has only the unknown X
01:06 Isolate X
01:17 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

Find the value of the parameter X

746x+3=8x+5x18 74-6x+3=8x+5x-18

2

Step-by-step solution

To solve for x x in the equation 746x+3=8x+5x18 74 - 6x + 3 = 8x + 5x - 18 , follow these steps:

  • Step 1: Simplify both sides of the equation.

On the left side:

746x+3=776x 74 - 6x + 3 = 77 - 6x (Combining the constants)

On the right side:

8x+5x18=13x18 8x + 5x - 18 = 13x - 18 (Combining the x x terms)

  • Step 2: Set the simplified expressions equal.

776x=13x18 77 - 6x = 13x - 18

  • Step 3: Rearrange the equation to isolate terms with x x .

Adding 6x 6x to both sides:

77=13x+6x18 77 = 13x + 6x - 18

77=19x18 77 = 19x - 18 (Combining the x x terms)

  • Step 4: Solve for x x .

Adding 18 to both sides to get rid of the constant on the right:

77+18=19x 77 + 18 = 19x

95=19x 95 = 19x

Dividing both sides by 19 to solve for x x :

x=9519=5 x = \frac{95}{19} = 5

Thus, the solution to the equation is x=5 x = 5 .

3

Final Answer

5 5

Key Points to Remember

Essential concepts to master this topic
  • Simplification: Combine like terms on each side before moving variables
  • Technique: Move all x terms to one side: 77 + 18 = 19x
  • Check: Substitute x = 5: 74 - 6(5) + 3 = 77 - 30 = 47 ✓

Common Mistakes

Avoid these frequent errors
  • Moving terms without changing signs
    Don't move -6x to the right as -6x instead of +6x = wrong coefficients! This creates incorrect calculations and wrong answers. Always change the sign when moving terms across the equals sign.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( x - 3 + 5 = 8 - 2 \)

FAQ

Everything you need to know about this question

Why do I need to simplify both sides first?

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Simplifying first makes the equation much easier to solve! Instead of dealing with 6 terms, you work with just 4 terms after combining like terms.

What if I move the x terms to the left side instead?

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That's perfectly fine! You can move terms to either side. Just remember to change signs when crossing the equals sign and you'll get the same answer.

How do I know which terms are like terms?

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Like terms have the same variable part. In this problem: 74 and 3 are constants, while 8x and 5x both have x, so they combine to 13x.

What if my final answer doesn't match any of the choices?

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Double-check your arithmetic! Make sure you combined like terms correctly:

  • Left side: 74 + 3 = 77
  • Right side: 8x + 5x = 13x

Can I solve this without moving terms around?

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You could try, but it's much harder! The standard method of isolating the variable by moving terms makes the solution clear and reduces errors.

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