Solve for r
r=\frac{y\left(7x+12\right)}{4}
y\neq 0
Solve for x
x=\frac{4r}{7y}-\frac{12}{7}
y\neq 0
Share
Copied to clipboard
4r=\frac{7}{4}x\times 4y+4y\times 3
Multiply both sides of the equation by 4y, the least common multiple of y,4.
4r=7xy+4y\times 3
Multiply \frac{7}{4} and 4 to get 7.
4r=7xy+12y
Multiply 4 and 3 to get 12.
\frac{4r}{4}=\frac{y\left(7x+12\right)}{4}
Divide both sides by 4.
r=\frac{y\left(7x+12\right)}{4}
Dividing by 4 undoes the multiplication by 4.
r=\frac{7xy}{4}+3y
Divide y\left(12+7x\right) by 4.
4r=\frac{7}{4}x\times 4y+4y\times 3
Multiply both sides of the equation by 4y, the least common multiple of y,4.
4r=7xy+4y\times 3
Multiply \frac{7}{4} and 4 to get 7.
4r=7xy+12y
Multiply 4 and 3 to get 12.
7xy+12y=4r
Swap sides so that all variable terms are on the left hand side.
7xy=4r-12y
Subtract 12y from both sides.
7yx=4r-12y
The equation is in standard form.
\frac{7yx}{7y}=\frac{4r-12y}{7y}
Divide both sides by 7y.
x=\frac{4r-12y}{7y}
Dividing by 7y undoes the multiplication by 7y.
x=\frac{4r}{7y}-\frac{12}{7}
Divide 4r-12y by 7y.
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}