Solve for X in the Linear Equation: 5x+4=7x

Linear Equations with Variable Terms

Solve for X:

5x+4=7x 5x+4=7x

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Step-by-step video solution

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00:00 Solve
00:04 Isolate the unknown X
00:20 Simplify what we can
00:42 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Solve for X:

5x+4=7x 5x+4=7x

2

Step-by-step solution

To solve the equation 5x+4=7x 5x + 4 = 7x , we will proceed as follows:

  • Step 1: Subtract 5x 5x from both sides to simplify the equation.

The equation is:
5x+45x=7x5x 5x + 4 - 5x = 7x - 5x

This simplifies to:
4=2x 4 = 2x

  • Step 2: To solve for x x , divide both sides by 2 to isolate x x .

Perform the division:
42=2x2 \frac{4}{2} = \frac{2x}{2}

This gives us:
2=x 2 = x

Therefore, the solution to the equation is x=2 x = 2 .

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Move all variable terms to one side first
  • Technique: Subtract 5x 5x from both sides: 4=2x 4 = 2x
  • Check: Substitute x=2 x = 2 back: 5(2)+4=7(2) 5(2) + 4 = 7(2) gives 14=14 14 = 14

Common Mistakes

Avoid these frequent errors
  • Subtracting different amounts from each side
    Don't subtract 5x from the left and 7x from the right = unequal operations! This violates the balance principle and gives completely wrong answers. Always subtract the same amount from both sides to maintain equality.

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 subtract 5x instead of 7x from both sides?

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You can subtract either! The goal is to get all variable terms on one side. Subtracting 5x 5x gives 4=2x 4 = 2x , while subtracting 7x 7x gives 2x+4=0 -2x + 4 = 0 . Both work!

What if I move the constant term instead of the variable?

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That works too! Subtract 4 from both sides first: 5x=7x4 5x = 7x - 4 . Then subtract 7x 7x : 2x=4 -2x = -4 . Divide by -2 to get the same answer: x=2 x = 2 .

How do I know which side to move the variables to?

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Choose the side that will give you a positive coefficient for the variable. This makes the final division step easier and reduces sign errors.

What if both sides have the same variable term?

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If you have something like 3x+5=3x+2 3x + 5 = 3x + 2 , subtracting 3x 3x from both sides gives 5=2 5 = 2 , which is impossible. This means no solution exists!

Can I check my answer a different way?

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Yes! You can also graph both sides as separate equations and see where they intersect. The x-coordinate of the intersection point is your solution.

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