Solve for X: Finding the Solution to x/4 + 2x - 18 = 0

Q: Why multiply the whole equation by 4 instead of just the fraction?

You must maintain equation balance! Whatever you do to one side, you must do to the other. Multiplying the entire equation by 4 eliminates fractions while keeping both sides equal.

Q: How do I combine like terms after clearing fractions?

Look for terms with the same variable and power. In $ x + 8x - 72 = 0 $, combine x + 8x = 9x to get $ 9x - 72 = 0 $.

Q: How do I verify my answer is correct?

Substitute x = 8 into the original equation: $ \frac{8}{4} + 2(8) - 18 = 2 + 16 - 18 = 0 $. Since you get 0 = 0, the answer is correct!

Linear Equations with Fractional Coefficients

$\frac{x}{4}+2x-18=0$

$x=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:08 We'll multiply by the denominator to eliminate the fraction

00:20 We'll simplify as much as possible

00:34 We'll arrange the equation so that one side has only the unknown X

00:42 We'll isolate the unknown X

00:53 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

$\frac{x}{4}+2x-18=0$

$x=\text{?}$

Step-by-step solution

To solve the equation $\frac{x}{4} + 2x - 18 = 0$ , we proceed as follows:

Step 1: Eliminate the fraction by multiplying the entire equation by 4:
$(4) \Big(\frac{x}{4} + 2x - 18\Big) = (4)(0)$
Step 2: Distribute and simplify:
$x + 8x - 72 = 0$
Step 3: Combine like terms:
$9x - 72 = 0$
Step 4: Isolate $9x$ by adding 72 to both sides:
$9x = 72$
Step 5: Solve for $x$ by dividing both sides by 9:
$x = \frac{72}{9}$
Step 6: Simplify the division:
$x = 8$

Thus, the solution to the problem is $x = 8$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Fraction Elimination: Multiply entire equation by 4 to clear denominators
Technique: $\frac{x}{4} + 2x - 18 = 0$ becomes $x + 8x - 72 = 0$
Check: Substitute x = 8: $\frac{8}{4} + 2(8) - 18 = 2 + 16 - 18 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the fraction term by 4
Don't multiply just $\frac{x}{4}$ by 4 and leave 2x - 18 unchanged = unbalanced equation! This breaks the equality and gives wrong answers. Always multiply every single term on both sides by the LCD.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why multiply the whole equation by 4 instead of just the fraction?

You must maintain equation balance! Whatever you do to one side, you must do to the other. Multiplying the entire equation by 4 eliminates fractions while keeping both sides equal.

What if I forget to multiply one of the terms by 4?

You'll get the wrong answer! For example, if you only clear the fraction: $x + 2x - 18 = 0$ gives x = 6, but substituting back shows this doesn't work in the original equation.

How do I combine like terms after clearing fractions?

Look for terms with the same variable and power. In $x + 8x - 72 = 0$ , combine x + 8x = 9x to get $9x - 72 = 0$ .

Is there another way to solve this without clearing fractions first?

Yes, but it's much harder! You could isolate the fraction term first, but clearing fractions by multiplying by the LCD is the most efficient method for equations like this.

How do I verify my answer is correct?

Substitute x = 8 into the original equation: $\frac{8}{4} + 2(8) - 18 = 2 + 16 - 18 = 0$ . Since you get 0 = 0, the answer is correct!

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