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 the equation

\( 5x-15=30 \)

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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