Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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-15x-10-\left(x-3\right)=-4\left(4x+5\right)+13
Use the distributive property to multiply 5 by -3x-2.
-15x-10-x-\left(-3\right)=-4\left(4x+5\right)+13
To find the opposite of x-3, find the opposite of each term.
-15x-10-x+3=-4\left(4x+5\right)+13
The opposite of -3 is 3.
-16x-10+3=-4\left(4x+5\right)+13
Combine -15x and -x to get -16x.
-16x-7=-4\left(4x+5\right)+13
Add -10 and 3 to get -7.
-16x-7=-16x-20+13
Use the distributive property to multiply -4 by 4x+5.
-16x-7=-16x-7
Add -20 and 13 to get -7.
-16x-7+16x=-7
Add 16x to both sides.
-7=-7
Combine -16x and 16x to get 0.
\text{true}
Compare -7 and -7.
x\in \mathrm{C}
This is true for any x.
-15x-10-\left(x-3\right)=-4\left(4x+5\right)+13
Use the distributive property to multiply 5 by -3x-2.
-15x-10-x-\left(-3\right)=-4\left(4x+5\right)+13
To find the opposite of x-3, find the opposite of each term.
-15x-10-x+3=-4\left(4x+5\right)+13
The opposite of -3 is 3.
-16x-10+3=-4\left(4x+5\right)+13
Combine -15x and -x to get -16x.
-16x-7=-4\left(4x+5\right)+13
Add -10 and 3 to get -7.
-16x-7=-16x-20+13
Use the distributive property to multiply -4 by 4x+5.
-16x-7=-16x-7
Add -20 and 13 to get -7.
-16x-7+16x=-7
Add 16x to both sides.
-7=-7
Combine -16x and 16x to get 0.
\text{true}
Compare -7 and -7.
x\in \mathrm{R}
This is true for any x.
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}