Solve for f
f\leq -4
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-3\geq f+1
Multiply both sides by 3. Since 3 is positive, the inequality direction remains the same.
f+1\leq -3
Swap sides so that all variable terms are on the left hand side. This changes the sign direction.
f\leq -3-1
Subtract 1 from both sides.
f\leq -4
Subtract 1 from -3 to get -4.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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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
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Limits
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