Question
Mathematics
$\frac{4}{11}x+\frac{1}{4}=\frac{1}{8}$(4)/(11)x+(1)/(4)=(1)/(8)
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To solve for $x$x in the equation $\frac{4}{11}x+\frac{1}{4}=\frac{1}{8}$(4)/(11)x+(1)/(4)=(1)/(8), we need to isolate the variable $x$x.
First, let’s subtract $\frac{1}{4}$(1)/(4) from both sides:
$\frac{4}{11}x+\frac{1}{4}-\frac{1}{4}=\frac{1}{8}-\frac{1}{4}$(4)/(11)x+(1)/(4)-(1)/(4)=(1)/(8)-(1)/(4)
Simplifying:
$\frac{4}{11}x=\frac{1}{8}-\frac{2}{8}$(4)/(11)x=(1)/(8)-(2)/(8)
Combining the fractions on the right side:
$\frac{4}{11}x=-\frac{1}{8}$(4)/(11)x=-(1)/(8)
Next, let’s multiply both sides by $\frac{11}{4}$(11)/(4) to eliminate the fraction:
$\frac{11}{4}\cdot \left(\frac{4}{11}x\right)=\frac{11}{4}\cdot \left(-\frac{1}{8}\right)$(11)/(4)*((4)/(11)x)=(11)/(4)*(-(1)/(8))
Simplifying:
$x=-\frac{11}{32}$x=-(11)/(32)
Therefore, $x=-\frac{11}{32}$x=-(11)/(32).
The solution is $x=-\frac{11}{32}$x=-(11)/(32).
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