Solve for x
x=-\frac{2}{3}\approx -0.666666667
Graph
Share
Copied to clipboard
\frac{2}{3}x+\frac{2}{3}\left(-4\right)=-\frac{7}{12}\left(x+6\right)
Use the distributive property to multiply \frac{2}{3} by x-4.
\frac{2}{3}x+\frac{2\left(-4\right)}{3}=-\frac{7}{12}\left(x+6\right)
Express \frac{2}{3}\left(-4\right) as a single fraction.
\frac{2}{3}x+\frac{-8}{3}=-\frac{7}{12}\left(x+6\right)
Multiply 2 and -4 to get -8.
\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}\left(x+6\right)
Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.
\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x-\frac{7}{12}\times 6
Use the distributive property to multiply -\frac{7}{12} by x+6.
\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x+\frac{-7\times 6}{12}
Express -\frac{7}{12}\times 6 as a single fraction.
\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x+\frac{-42}{12}
Multiply -7 and 6 to get -42.
\frac{2}{3}x-\frac{8}{3}=-\frac{7}{12}x-\frac{7}{2}
Reduce the fraction \frac{-42}{12} to lowest terms by extracting and canceling out 6.
\frac{2}{3}x-\frac{8}{3}+\frac{7}{12}x=-\frac{7}{2}
Add \frac{7}{12}x to both sides.
\frac{5}{4}x-\frac{8}{3}=-\frac{7}{2}
Combine \frac{2}{3}x and \frac{7}{12}x to get \frac{5}{4}x.
\frac{5}{4}x=-\frac{7}{2}+\frac{8}{3}
Add \frac{8}{3} to both sides.
\frac{5}{4}x=-\frac{21}{6}+\frac{16}{6}
Least common multiple of 2 and 3 is 6. Convert -\frac{7}{2} and \frac{8}{3} to fractions with denominator 6.
\frac{5}{4}x=\frac{-21+16}{6}
Since -\frac{21}{6} and \frac{16}{6} have the same denominator, add them by adding their numerators.
\frac{5}{4}x=-\frac{5}{6}
Add -21 and 16 to get -5.
x=-\frac{5}{6}\times \frac{4}{5}
Multiply both sides by \frac{4}{5}, the reciprocal of \frac{5}{4}.
x=\frac{-5\times 4}{6\times 5}
Multiply -\frac{5}{6} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.
x=\frac{-20}{30}
Do the multiplications in the fraction \frac{-5\times 4}{6\times 5}.
x=-\frac{2}{3}
Reduce the fraction \frac{-20}{30} to lowest terms by extracting and canceling out 10.
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}