Solve for y
y<0
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30y+15y<5y+3y
Multiply both sides of the equation by 15. Since 15 is positive, the inequality direction remains the same.
45y<5y+3y
Combine 30y and 15y to get 45y.
45y<8y
Combine 5y and 3y to get 8y.
45y-8y<0
Subtract 8y from both sides.
37y<0
Combine 45y and -8y to get 37y.
y<0
Product of two numbers is <0 if one is >0 and the other is <0. Since 37>0, y must be <0.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}