# Unit 07: Linear Equations and Inequalities

These notes are send by Mr. **Malik Faisal Rafiq**. We are very thankful to him for sending these notes.

**Linear Equations:** A linear equation is one unknown variable $x$ is an equation of the form $ax+b=0$, where $a,b\in \mathbb{R}$ and $a\neq 0$.

**Radical Equations:** When the variable in an equation occurs under a radical, the equation is called radical equation.

**Equation Involving Absolute Value:** The absolute value of real number $a$ denoted by $|a|$ is defined as
$$
|a|=\left\{\begin{matrix}
a & \text{if } a\geq 0, \\
-a & \text{if } a<0.
\end{matrix}\right.
$$
e.g. $|6|=6$, $|0|=0$, $|-3|=3$.

**Defining inequalities:** Let $a,b$ be real numbers. Then $a$ is greater than $b$ if the difference $a-b>0$ and we denote this order relation by the inequality $a>b$. An equivalent statement is that $b$ is less than $a$, symbolized by $b<a$.

### Solutions

- Exercise 7.1 | View Online | Download PDF (178.7 KiB, 1938 downloads)

- Exercise 7.2 | View Online | Download PDF (101.93 KiB, 1276 downloads)

- Exercise 7.3 | View Online | Download PDF (115.41 KiB, 1356 downloads)

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