Solve for x
x=\frac{4\lambda +35}{2\lambda -7}
\lambda \neq \frac{7}{2}
Solve for λ
\lambda =\frac{7\left(x+5\right)}{2\left(x-2\right)}
x\neq 2
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2\lambda \left(x-2\right)-7\left(x+3\right)=14
Multiply both sides of the equation by 14, the least common multiple of 7,2.
2\lambda x-4\lambda -7\left(x+3\right)=14
Use the distributive property to multiply 2\lambda by x-2.
2\lambda x-4\lambda -7x-21=14
Use the distributive property to multiply -7 by x+3.
2\lambda x-7x-21=14+4\lambda
Add 4\lambda to both sides.
2\lambda x-7x=14+4\lambda +21
Add 21 to both sides.
2\lambda x-7x=35+4\lambda
Add 14 and 21 to get 35.
\left(2\lambda -7\right)x=35+4\lambda
Combine all terms containing x.
\left(2\lambda -7\right)x=4\lambda +35
The equation is in standard form.
\frac{\left(2\lambda -7\right)x}{2\lambda -7}=\frac{4\lambda +35}{2\lambda -7}
Divide both sides by 2\lambda -7.
x=\frac{4\lambda +35}{2\lambda -7}
Dividing by 2\lambda -7 undoes the multiplication by 2\lambda -7.
2\lambda \left(x-2\right)-7\left(x+3\right)=14
Multiply both sides of the equation by 14, the least common multiple of 7,2.
2\lambda x-4\lambda -7\left(x+3\right)=14
Use the distributive property to multiply 2\lambda by x-2.
2\lambda x-4\lambda -7x-21=14
Use the distributive property to multiply -7 by x+3.
2\lambda x-4\lambda -21=14+7x
Add 7x to both sides.
2\lambda x-4\lambda =14+7x+21
Add 21 to both sides.
2\lambda x-4\lambda =35+7x
Add 14 and 21 to get 35.
\left(2x-4\right)\lambda =35+7x
Combine all terms containing \lambda .
\left(2x-4\right)\lambda =7x+35
The equation is in standard form.
\frac{\left(2x-4\right)\lambda }{2x-4}=\frac{7x+35}{2x-4}
Divide both sides by 2x-4.
\lambda =\frac{7x+35}{2x-4}
Dividing by 2x-4 undoes the multiplication by 2x-4.
\lambda =\frac{7\left(x+5\right)}{2\left(x-2\right)}
Divide 35+7x by 2x-4.
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