Solve the Fraction Equation: Finding X in (1/2)(x+3)=0

Linear Equations with Zero Products

Solve for X:

12(x+3)=0 \frac{1}{2}(x+3)=0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's find X! Are you ready?
00:09 First, multiply everything by 2 to get rid of the fraction. Great job!
00:22 Next, simplify what we can. Keep going!
00:28 Now, arrange the terms so X is on one side by itself. You're almost there!
00:35 And that's it! We've found X is the solution. Fantastic work!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve for X:

12(x+3)=0 \frac{1}{2}(x+3)=0

2

Step-by-step solution

To solve for x x in the equation 12(x+3)=0 \frac{1}{2}(x+3) = 0 , we will take the following steps:

  • Step 1: Eliminate the fraction by multiplying both sides of the equation by 2.

  • Step 2: Simplify the resulting equation to isolate the variable x x .

Let's carry out these steps:
Step 1: Multiply both sides by 2:
⇒2×12(x+3)=2×0\Rightarrow 2 \times \frac{1}{2}(x + 3) = 2 \times 0
⇒x+3=0\Rightarrow x + 3 = 0

Step 2: Solve the equation x+3=0 x + 3 = 0 for x x :
Subtract 3 from both sides:
⇒x=0−3\Rightarrow x = 0 - 3
⇒x=−3\Rightarrow x = -3

Therefore, the solution to the equation is x=−3 x = -3 .

3

Final Answer

3-

Key Points to Remember

Essential concepts to master this topic
  • Zero Product Rule: When a product equals zero, one factor must be zero
  • Technique: If 12(x+3)=0 \frac{1}{2}(x+3) = 0 , then x+3 must equal 0
  • Check: Substitute x = -3: 12(−3+3)=12(0)=0 \frac{1}{2}(-3+3) = \frac{1}{2}(0) = 0 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing both sides by the fraction coefficient first
    Don't divide by 12 \frac{1}{2} to get 2(x+3) = 0 = complicated steps! This creates unnecessary work and potential errors. Always recognize that if a product equals zero, one factor must be zero, so x+3 = 0 directly.

Practice Quiz

Test your knowledge with interactive questions

Solve for x:

\( 2(4-x)=8 \)

FAQ

Everything you need to know about this question

Why can I ignore the fraction 12 \frac{1}{2} and just solve x+3 = 0?

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Because any number times zero equals zero! Since 12≠0 \frac{1}{2} \neq 0 , the only way for 12(x+3)=0 \frac{1}{2}(x+3) = 0 is if (x+3) = 0.

What if I multiply both sides by 2 first?

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That works too! You'd get x+3=0 x+3 = 0 , which is the same result. Both methods are correct, but recognizing the zero product pattern is faster.

Could x equal something other than -3?

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No, this equation has exactly one solution. Since we need x+3 = 0, there's only one value of x that makes this true: x=−3 x = -3 .

How do I know when to use the zero product rule?

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Look for equations where something times something equals zero. If you see a product (multiplication) on one side and zero on the other, one of the factors must equal zero!

What if the coefficient was a different fraction like 34 \frac{3}{4} ?

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The same rule applies! As long as the coefficient isn't zero, you can set the other factor equal to zero. So 34(x+3)=0 \frac{3}{4}(x+3) = 0 still gives us x+3 = 0.

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