Solve the Equation: Determining X in $- \frac{5+7x}{2} = 22$

Q: Why do I multiply both sides by 2 instead of just cross-multiplying?

Since we have $ \frac{-5+7x}{2}=22 $, multiplying both sides by 2 is the most direct approach. This eliminates the fraction immediately and gives us $ -5+7x=44 $.

Q: What if I forget to add 5 to both sides in step 2?

If you skip adding 5, you'll have $ 7x = 44 - 5 $ instead of $ 7x = 49 $. This gives x = 39/7, which is wrong! Always isolate the x-term by moving constants to the other side.

Q: How do I know I'm solving correctly when there's a negative sign?

The negative sign in $ -5+7x $ stays with the 5. When you add 5 to both sides, -5 + 5 = 0, leaving just $ 7x $ on the left side.

Q: Can I check my answer a different way?

Yes! You can also work backwards: if x = 7, then $ 7x = 49 $, so $ -5 + 49 = 44 $, and $ \frac{44}{2} = 22 $ ✓

Linear Equations with Fraction Elimination

$\frac{-5+7x}{2}=22$

How much is X worth?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Multiply both sides by 2 to eliminate the denominator

00:23 Add 5 to both sides to isolate the variable

00:44 Divide both sides by 7 to find the value of one variable

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{-5+7x}{2}=22$

How much is X worth?

Step-by-step solution

To solve this linear equation, we'll take the following steps:

Step 1: Multiply both sides of the equation by 2 to eliminate the fraction.
Step 2: Simplify and isolate the term containing $x$ .
Step 3: Solve for $x$ by further isolation.

Let's execute these steps:

Step 1: Start with the given equation:

$\frac{-5 + 7x}{2} = 22$

Multiply both sides by 2 to remove the fraction:

$-5 + 7x = 44$

Step 2: Now, eliminate the constant term on the left side by adding 5 to both sides:

$-5 + 7x + 5 = 44 + 5$

This simplifies to:

$7x = 49$

Step 3: Finally, solve for $x$ by dividing both sides by 7:

$x = \frac{49}{7}$

Calculate the result:

$x = 7$

Therefore, the value of $x$ is $x = 7$ .

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by 2 to eliminate the fraction
Technique: Transform $\frac{-5+7x}{2}=22$ to $-5+7x=44$
Check: Substitute x=7: $\frac{-5+7(7)}{2}=\frac{44}{2}=22$ ✓

Common Mistakes

Avoid these frequent errors

Multiplying only the numerator by 2
Don't multiply just the numerator -5+7x by 2 and leave the right side as 22 = wrong equation! This creates an unbalanced equation because you're not applying the same operation to both sides. Always multiply the entire right side by the same number when clearing fractions.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 5x=25 $$

FAQ

Everything you need to know about this question

Why do I multiply both sides by 2 instead of just cross-multiplying?

Since we have $\frac{-5+7x}{2}=22$ , multiplying both sides by 2 is the most direct approach. This eliminates the fraction immediately and gives us $-5+7x=44$ .

What if I forget to add 5 to both sides in step 2?

If you skip adding 5, you'll have $7x = 44 - 5$ instead of $7x = 49$ . This gives x = 39/7, which is wrong! Always isolate the x-term by moving constants to the other side.

How do I know I'm solving correctly when there's a negative sign?

The negative sign in $-5+7x$ stays with the 5. When you add 5 to both sides, -5 + 5 = 0, leaving just $7x$ on the left side.

Can I check my answer a different way?

Yes! You can also work backwards: if x = 7, then $7x = 49$ , so $-5 + 49 = 44$ , and $\frac{44}{2} = 22$ ✓

What if I get confused with the order of operations?

Remember: once you clear the fraction, treat it like any linear equation. First add/subtract to isolate the x-term, then divide to solve for x.

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Solve the Equation: Determining X in \(- \frac{5+7x}{2} = 22\)