Linear Inequalities in One Variable

7.2  Linear Inequalities in One Variable
Symbol \(\geq\) Symbol \(\leq\)
  • At least
  • Not less than
  • Minimum
  • At most
  • Not more than
  • Maximum

Construct the linear inequality:

The price, \(\text{RM}x\), of a double-storey terrace house is \(\text{RM}450\,000\) and above.

The linear inequality is,

\(x\geq 450\,000\).

Solve problems involving linear inequalities in one variable:
  • Linear inequality in one variable is an unequal relationship between a number and a variable with power of \(1\).
  • Has more than one possible solution.

Calculate: \(16-5x\leq -4\)

\(\begin{aligned} 16-5x&\leq -4 \\\\16-5x-16&\leq -4-16 \\\\-5x&\leq -20 \\\\\dfrac{-5x}{-5}&\geq \dfrac{-20}{-5} \\\\x&\geq 4. \end{aligned}\)

Solve simultaneous linear inequalities in one variable:


\(8x+5\geq 5x-13\) and

\(3x-4\gt 9x+20\).

\(\begin{aligned}8x+5&\geq 5x-13 \\\\8x-5x&\geq-13-5 \\\\3x&\geq-18 \\\\x&\geq -6.\\\\ \end{aligned}\)

\(\begin{aligned}3x-4&\gt 9x+20 \\\\3x-9x&\gt20+4 \\\\-6x&\gt24 \\\\x&\lt-4.\\\\ \end{aligned}\)

Thus, the solution is

\(-6\leq x \lt -4\).