Solve for x
x\leq -16
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15x-3\left(2-x\right)\geq 5\left(4x+1\right)-\left(x-5\right)
Multiply both sides of the equation by 15, the least common multiple of 5,3,15. Since 15 is positive, the inequality direction remains the same.
15x-6+3x\geq 5\left(4x+1\right)-\left(x-5\right)
Use the distributive property to multiply -3 by 2-x.
18x-6\geq 5\left(4x+1\right)-\left(x-5\right)
Combine 15x and 3x to get 18x.
18x-6\geq 20x+5-\left(x-5\right)
Use the distributive property to multiply 5 by 4x+1.
18x-6\geq 20x+5-x-\left(-5\right)
To find the opposite of x-5, find the opposite of each term.
18x-6\geq 20x+5-x+5
The opposite of -5 is 5.
18x-6\geq 19x+5+5
Combine 20x and -x to get 19x.
18x-6\geq 19x+10
Add 5 and 5 to get 10.
18x-6-19x\geq 10
Subtract 19x from both sides.
-x-6\geq 10
Combine 18x and -19x to get -x.
-x\geq 10+6
Add 6 to both sides.
-x\geq 16
Add 10 and 6 to get 16.
x\leq -16
Divide both sides by -1. Since -1 is negative, the inequality direction is changed.
Examples
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{ 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}