Algebra equations are equations that contain variables. Variables are symbols that represent unknown quantities. Algebra equations can be used to model many different real-world situations. For example, we can use algebra equations to calculate the price of items, the distance between two points, or the area of a triangle.

**Types of Algebra Equations**

There are many different types of algebra equations, but some of the most common include:

**Linear equations:**Linear equations are equations of the form $ax + b = c$, where $a$, $b$, and $c$ are constants and $x$ is the variable.**Quadratic equations:**Quadratic equations are equations of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants and $x$ is the variable.**Rational equations:**Rational equations are equations that contain fractions.**Radical equations:**Radical equations are equations that contain radicals.

**Solving Algebra Equations**

There are many different ways to solve algebra equations, depending on the type of equation. Some of the most common methods include:

**Isolating the variable:**This method involves using algebraic operations to manipulate the equation so that the variable is isolated on one side of the equation.**Factoring:**This method involves factoring the equation into two or more smaller equations, which are then easier to solve.**Using the quadratic formula:**This formula can be used to solve quadratic equations.**Using graphing:**This method involves graphing the equation and then finding the solutions where the graph crosses the $x$-axis.

**Examples of Solving Algebra Equations**

Here are some examples of how to solve different types of algebra equations:

**Linear equation:**

$2x + 3 = 7$

To solve this equation, we can isolate the variable $x$ by subtracting $3$ from both sides and then dividing both sides by $2$.

```
2x + 3 = 7
2x = 7 - 3
2x = 4
x = 2
```

**Quadratic equation:**

$x^2 + 2x – 3 = 0$

To solve this equation, we can factor it into two smaller equations: $(x + 3)(x – 1) = 0$. We then set each factor equal to zero and solve for $x$.

```
(x + 3)(x - 1) = 0
x + 3 = 0 or x - 1 = 0
x = -3 or x = 1
```

**Rational equation:**

$\dfrac{x}{x + 1} = \dfrac{1}{x – 2}$

To solve this equation, we can multiply both sides by the common denominator, $x(x + 1)(x – 2)$. This gives us the equation:

```
x = x - 2
0 = -2
```

This equation has no solution, so the rational equation has no solution.

**Radical equation:**

$\sqrt{x + 2} = 3$

To solve this equation, we can square both sides to get rid of the radical.

```
√x + 2 = 3
(√x + 2)^2 = 3^2
x + 2 = 9
x = 7
```