Adding or subtracting the same quantity keeps the inequality direction. Multiplication or division by a positive number also keeps it. Multiplication or division by a negative number reverses it: 2<5, but -2>-5. Example 7-3x>16 -3x>9 x<-3. The last step divides by -3, so the sign reverses. A check value such as x=-4 gives 19>16; the boundary x=-3 gives equality and is excluded. Keep exact boundaries. For example, x< 23 is not the same set as x<0.67.

Adding or subtracting the same quantity keeps the inequality direction. Multiplication or division by a positive number also keeps it. Multiplication or division by a negative number reverses it: \(2<5\), but \(-2>-5\).

\(\begin{aligned}7-3x&>16\\-3x&>9\\x&<-3.\end{aligned}\)

The last step divides by \(-3\), so the sign reverses. A check value such as \(x=-4\) gives \(19>16\); the boundary \(x=-3\) gives equality and is excluded.

Keep exact boundaries. For example, \(x<\dfrac23\) is not the same set as \(x<0.67\).

Solving linear inequalities

Solving linear inequalities