Solve for X:
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Solve for X:
To solve the equation , we'll follow these steps:
Step 1: Use cross-multiplication to eliminate the fractions.
Step 2: Simplify the resulting linear equation.
Step 3: Solve for .
Now, let's work through each step:
Step 1: Cross-multiply to clear the fractions:
Cross-multiplying gives:
Step 2: Distribute the 9 on the left side:
Step 3: Isolate the variable :
Subtract from both sides:
This simplifies to:
Subtract 18 from both sides:
Divide by 6 to solve for :
Therefore, .
The solution to the problem is .
Solve for X:
\( x - 3 + 5 = 8 - 2 \)
Cross-multiplication works when you have one fraction equals another fraction, like . It's perfect for rational equations but won't work if you have addition or subtraction between fractions.
Negative solutions are completely normal in algebra! Just make sure to check your work by substituting back. As long as the denominators aren't zero, negative answers are valid.
Always check that your answer doesn't make any denominator equal zero. In this problem, x = -3 makes the first denominator -3 (not zero) and the second denominator -1 (not zero), so it's valid!
Distribution is required because you have multiplication across parentheses. You can't cancel or skip this step - it's like saying 9 × (5+3) equals 9 × 5, which isn't true!
Yes! You could multiply both sides by to clear fractions, but cross-multiplication is usually faster and cleaner for equations with two fractions.
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