Solve the Linear Equation Involving a Fraction: -7x + 3 - 1/2 = 0

Q: Why do I need to convert 3 to a fraction?

Converting 3 to $ \frac{6}{2} $ gives you a common denominator with $ \frac{1}{2} $. This makes subtraction much easier: $ \frac{6}{2} - \frac{1}{2} = \frac{5}{2} $!

Q: Can I use decimals instead of fractions?

You could convert $ \frac{1}{2} $ to 0.5, but keeping everything as fractions usually gives you exact answers without rounding errors. Fractions are more precise!

Q: How do I divide by a negative number?

When dividing both sides by -7, remember that dividing by a negative flips the sign. So $ \frac{-\frac{5}{2}}{-7} $ becomes positive: $ \frac{5}{14} $.

Q: What if I get confused with all the fractions?

Take it step by step! First combine constants, then isolate the variable term, finally divide. Write each step clearly and double-check your fraction arithmetic.

Linear Equations with Mixed Number Operations

Calculate the value of x:

$-7x+3-\frac{1}{2}=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find the value of X.

00:09 First, arrange the equation so that X is alone on one side.

00:21 Next, find a common denominator and multiply everything by it.

00:38 Now, collect all like terms together.

00:47 Isolate X by multiplying both sides by the reciprocal.

00:57 Remember, multiply numerator by numerator, and denominator by denominator.

01:02 And there you have it! That's how you solve for X.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the value of x:

$-7x+3-\frac{1}{2}=0$

Step-by-step solution

To solve the equation $-7x + 3 - \frac{1}{2} = 0$ , follow these steps:

Step 1: Simplify the equation.
First, combine the constant terms $3$ and $-\frac{1}{2}$ . Convert $3$ to a fraction as $\frac{6}{2}$ to facilitate subtraction. Thus, $3 - \frac{1}{2} = \frac{6}{2} - \frac{1}{2} = \frac{5}{2}$ .
The equation now becomes: $-7x + \frac{5}{2} = 0$ .

Step 2: Move the constant term to the other side.
Subtract $\frac{5}{2}$ from both sides:
$-7x + \frac{5}{2} - \frac{5}{2} = 0 - \frac{5}{2}$ .
This simplifies to: $-7x = -\frac{5}{2}$ .

Step 3: Isolate $x$ .
Divide both sides by $-7$ to solve for $x$ :
$x = \frac{-\frac{5}{2}}{-7}$ .
Simplify the expression:
$x = \frac{5}{14}$ .

Thus, the solution to the equation is $\boxed{\frac{5}{14}}$ , which corresponds to choice 3.

Final Answer

$\frac{5}{14}$

Key Points to Remember

Essential concepts to master this topic

Simplification: Combine constant terms before isolating the variable
Technique: Convert 3 to $\frac{6}{2}$ so $3 - \frac{1}{2} = \frac{5}{2}$
Check: Substitute $x = \frac{5}{14}$ : $-7(\frac{5}{14}) + 3 - \frac{1}{2} = 0$ ✓

Common Mistakes

Avoid these frequent errors

Adding fractions with different denominators incorrectly
Don't add 3 - 1/2 = 2.5 using decimals = wrong simplified equation! This creates calculation errors and messy arithmetic. Always convert whole numbers to fractions with common denominators first.

Practice Quiz

Test your knowledge with interactive questions

$$ x+x=8 $$

FAQ

Everything you need to know about this question

Why do I need to convert 3 to a fraction?

Converting 3 to $\frac{6}{2}$ gives you a common denominator with $\frac{1}{2}$ . This makes subtraction much easier: $\frac{6}{2} - \frac{1}{2} = \frac{5}{2}$ !

Can I use decimals instead of fractions?

You could convert $\frac{1}{2}$ to 0.5, but keeping everything as fractions usually gives you exact answers without rounding errors. Fractions are more precise!

How do I divide by a negative number?

When dividing both sides by -7, remember that dividing by a negative flips the sign. So $\frac{-\frac{5}{2}}{-7}$ becomes positive: $\frac{5}{14}$ .

What if I get confused with all the fractions?

Take it step by step! First combine constants, then isolate the variable term, finally divide. Write each step clearly and double-check your fraction arithmetic.

Is there a faster way to solve this?

You could multiply the entire equation by 2 first to clear the fraction: $2(-7x + 3 - \frac{1}{2}) = 2(0)$ gives $-14x + 6 - 1 = 0$ , then solve normally.

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