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Question
Math
Posted 6 months ago

Solve for xx.
−8x+3=−52x+6+2
-\frac{8}{x+3}=-\frac{5}{2 x+6}+2


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Answer from Sia
Posted 6 months ago
Solution by Steps
step 1
Start with the given equation: −8x+3=−52x+6+2-\frac{8}{x+3} = -\frac{5}{2x+6} + 2
step 2
Notice that 2x+62x + 6 can be rewritten as 2(x+3)2(x + 3). So, the equation becomes: −8x+3=−52(x+3)+2-\frac{8}{x+3} = -\frac{5}{2(x+3)} + 2
step 3
To eliminate the fractions, multiply both sides by 2(x+3)2(x+3): −8⋅2=−5+2⋅2(x+3)⋅(x+3)-8 \cdot 2 = -5 + 2 \cdot 2(x+3) \cdot (x+3)
step 4
Simplify the equation: −16=−5+4(x+3)-16 = -5 + 4(x+3)
step 5
Add 5 to both sides: −16+5=4(x+3)-16 + 5 = 4(x+3)
step 6
Simplify: −11=4(x+3)-11 = 4(x+3)
step 7
Divide both sides by 4: −114=x+3-\frac{11}{4} = x + 3
step 8
Subtract 3 from both sides: x=−114−3x = -\frac{11}{4} - 3
step 9
Simplify the right side: x=−114−124=−234x = -\frac{11}{4} - \frac{12}{4} = -\frac{23}{4}
Answer
x=−234x = -\frac{23}{4}
Key Concept
Solving Rational Equations
Explanation
To solve rational equations, clear the fractions by multiplying both sides by the least common denominator (LCD), then solve the resulting linear equation.

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