## Understanding the Equation: (a+bc)(d−e)=f

The equation **(a+bc)(d−e)=f** represents a simple algebraic expression that relates several variables. It's a fundamental concept in algebra, and understanding its components and how it works is crucial for solving various problems.

### Breakdown of the Equation:

**Variables:**The equation involves six variables:**a, b, c, d, e, and f**. These variables can represent any numerical value.**Operations:**The equation uses basic arithmetic operations:**Addition:**`a + bc`

**Multiplication:**`(a + bc)(d - e)`

**Subtraction:**`d - e`

**Equality:**`=`

(signifies that both sides of the equation are equivalent)

**Parentheses:**Parentheses are used to indicate the order of operations. In this case,`(a + bc)`

and`(d - e)`

should be calculated first before multiplying them.

### Applications of the Equation:

This equation can be used in a variety of contexts, including:

**Solving for an unknown variable:**If we know the values of five variables, we can solve for the sixth variable. For example, if we know the values of a, b, c, d, and e, we can solve for f.**Simplifying algebraic expressions:**The equation can be used to simplify more complex algebraic expressions by substituting the expression`(a+bc)(d−e)`

with the variable`f`

.**Modeling real-world scenarios:**The equation can be used to model various real-world situations, such as calculating the total cost of a purchase (where a, b, and c represent unit prices, quantity, and discounts, respectively), or finding the net profit after deducting expenses (where d and e represent revenue and expenses, respectively).

### Solving the Equation:

To solve the equation for a specific variable, we need to follow these steps:

**Isolate the variable:**Use algebraic manipulations to isolate the variable you want to solve for on one side of the equation.**Simplify:**Simplify the expression by performing the necessary operations.**Substitute values:**Substitute the known values of the other variables to find the value of the desired variable.

**Example:**

Let's say we want to solve for `f`

in the equation `(a+bc)(d−e)=f`

, given that:

- a = 2
- b = 3
- c = 4
- d = 5
- e = 1

**Substitute:**We can substitute the values into the equation:`(2 + 3 * 4)(5 - 1) = f`

**Simplify:**`(2 + 12)(4) = f`

**Calculate:**`(14)(4) = f`

**Solve:**`56 = f`

Therefore, `f = 56`

.

By understanding the components and applications of this equation, we can effectively manipulate it to solve problems and model real-world situations in a variety of fields.