Question: Give me teachings on equations with examples and test to slove myself
1. **Understanding Equations**
An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.
2. **Basic Form**
A simple linear equation looks like $$ax + b = c$$ where $$a$$, $$b$$, and $$c$$ are constants, and $$x$$ is the variable.
3. **Solving Linear Equations**
To solve for $$x$$, isolate $$x$$ on one side:
$$ax + b = c$$
Subtract $$b$$ from both sides:
$$ax + \cancel{b} - \cancel{b} = c - b$$
$$ax = c - b$$
Divide both sides by $$a$$:
$$\frac{ax}{\cancel{a}} = \frac{c - b}{\cancel{a}}$$
$$x = \frac{c - b}{a}$$
4. **Example**
Solve $$3x + 4 = 19$$:
Subtract 4:
$$3x + \cancel{4} - \cancel{4} = 19 - 4$$
$$3x = 15$$
Divide by 3:
$$\frac{3x}{\cancel{3}} = \frac{15}{\cancel{3}}$$
$$x = 5$$
5. **Practice Test**
Solve the following equations:
- $$2x - 3 = 7$$
- $$5x + 10 = 0$$
- $$4x = 20$$
Try to isolate $$x$$ using the steps above and find the value of $$x$$.