Solve for z
z=15
Share
Copied to clipboard
15\times 2=15z\times \frac{1}{3}+15z\left(-\frac{1}{5}\right)
Variable z cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 15z, the least common multiple of z,3,5.
30=15z\times \frac{1}{3}+15z\left(-\frac{1}{5}\right)
Multiply 15 and 2 to get 30.
30=\frac{15}{3}z+15z\left(-\frac{1}{5}\right)
Multiply 15 and \frac{1}{3} to get \frac{15}{3}.
30=5z+15z\left(-\frac{1}{5}\right)
Divide 15 by 3 to get 5.
30=5z+\frac{15\left(-1\right)}{5}z
Express 15\left(-\frac{1}{5}\right) as a single fraction.
30=5z+\frac{-15}{5}z
Multiply 15 and -1 to get -15.
30=5z-3z
Divide -15 by 5 to get -3.
30=2z
Combine 5z and -3z to get 2z.
2z=30
Swap sides so that all variable terms are on the left hand side.
z=\frac{30}{2}
Divide both sides by 2.
z=15
Divide 30 by 2 to get 15.
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}