Solve for x
x\leq -7
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5x-3\leq -2x-52
Multiply both sides of the equation by -2. Since -2 is negative, the inequality direction is changed.
5x-3+2x\leq -52
Add 2x to both sides.
7x-3\leq -52
Combine 5x and 2x to get 7x.
7x\leq -52+3
Add 3 to both sides.
7x\leq -49
Add -52 and 3 to get -49.
x\leq \frac{-49}{7}
Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.
x\leq -7
Divide -49 by 7 to get -7.
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}