## 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 $$-6\leq x \lt -4$$.