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

Example

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.

Example

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:

Example

Solve:

\(8x+5\geq 5x-13\) 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

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