Solve for a
a<3
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2-a-\left(-5\right)>2a-2
To find the opposite of a-5, find the opposite of each term.
2-a+5>2a-2
The opposite of -5 is 5.
7-a>2a-2
Add 2 and 5 to get 7.
7-a-2a>-2
Subtract 2a from both sides.
7-3a>-2
Combine -a and -2a to get -3a.
-3a>-2-7
Subtract 7 from both sides.
-3a>-9
Subtract 7 from -2 to get -9.
a<\frac{-9}{-3}
Divide both sides by -3. Since -3 is negative, the inequality direction is changed.
a<3
Divide -9 by -3 to get 3.
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}