Solve for y (complex solution)
y\in \mathrm{C}
Solve for y
y\in \mathrm{R}
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5\left(y+2\right)+y-1=3\left(2y+3\right)
Multiply both sides of the equation by 15, the least common multiple of 3,15,5.
5y+10+y-1=3\left(2y+3\right)
Use the distributive property to multiply 5 by y+2.
6y+10-1=3\left(2y+3\right)
Combine 5y and y to get 6y.
6y+9=3\left(2y+3\right)
Subtract 1 from 10 to get 9.
6y+9=6y+9
Use the distributive property to multiply 3 by 2y+3.
6y+9-6y=9
Subtract 6y from both sides.
9=9
Combine 6y and -6y to get 0.
\text{true}
Compare 9 and 9.
y\in \mathrm{C}
This is true for any y.
5\left(y+2\right)+y-1=3\left(2y+3\right)
Multiply both sides of the equation by 15, the least common multiple of 3,15,5.
5y+10+y-1=3\left(2y+3\right)
Use the distributive property to multiply 5 by y+2.
6y+10-1=3\left(2y+3\right)
Combine 5y and y to get 6y.
6y+9=3\left(2y+3\right)
Subtract 1 from 10 to get 9.
6y+9=6y+9
Use the distributive property to multiply 3 by 2y+3.
6y+9-6y=9
Subtract 6y from both sides.
9=9
Combine 6y and -6y to get 0.
\text{true}
Compare 9 and 9.
y\in \mathrm{R}
This is true for any y.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}