**Equations, **such as **4(5-x) = 8, **hold a captivating allure in** mathematics** as they represent the delicate balance between** known** and **unknown quantities**. **Solving equations** is a powerful tool to unveil the hidden values within. Among the **myriad equations** that perplex and **engage mathematicians**, the equation **4(5-x) = 8** stands as an **intriguing puzzle** waiting to be solved.

In this article, we embark on a journey into the depths of this **equation**, unraveling the **methods** and **techniques** required to find the **elusive** value of **x** that satisfies the equation. By exploring the intricate steps of **equation-solving. **Join us as we navigate the twists and turns of solving the equation **4(5-x) = 8**, and witness the beauty of **mathematical problem-solving** unfold before your eyes.

**Defining 4(5-x) = 8**

**Solving the equation** **4(5-x) = 8** involves finding the value(s) of the variable **x** that make the equation **true**. The **equation** represents an **algebraic relationship** between the unknown variable **x** and **known quantities**, in this case, the numbers **4**, **5**, and **8**.

By performing a series of **algebraic manipulations** and **simplifications**, the goal is to determine the specific value(s) of **x** that satisfy the equation. **Solving equations** is a fundamental process in **mathematics** and serves as a vital tool in various applications, allowing us to discover unknown quantities and make mathematical connections.

By unraveling the mystery of equation **4(5-x) = 8**, we unlock a **gateway** to the world of **problem-solving** and unveil the solutions that bring clarity to the **mathematical** realm.

## Solving the Equation **4(5-x) = 8**

To solve the equation **4(5-x) = 8**, follow these steps:

### Step 1

**Distribute** the **4** on the left side of the **equation**: Multiply **4** by each term inside the **parentheses**.

4 * 5 – 4 * x = 8

20 – 4x = 8

### Step 2

**Simplify** the equation: Combine **like terms** by subtracting **20** from both sides.

20 – 20 – 4x = 8 – 20

-4x = -12

### Step 3

Divide both sides by **-4**: To **isolate** the variable **x**, **divide** both sides of the equation by **-4**.

(-4x) / -4 = (-12) / -4

x = 3

### Step 4

**Verify** the solution: To confirm that the **solution x = 3** is correct, substitute it back into the **original equation** and check if both sides are **equal**.

4(5 – 3) = 8

4(2) = 8

8 = 8

Since both sides of the equation are equal when** x = 3**, we can conclude that the **solution x = 3** satisfies the **original equation**.

Therefore, the **solution** to the equation **4(5-x) = 8** is **x = 3**.

## Applications

Solving the equation **4(5-x) = 8** has practical applications in various fields. Here are some examples:

### Physics and Engineering

**Equations** are vital in **physics** and **engineering**, where mathematical models describe physical phenomena. **Solving equations** helps determine unknown variables or quantities in various systems. In this context, **solving equations** like **4(5-x) = 8** allows engineers and physicists to find the values of variables involved in mathematical representations of physical processes. This can be useful for determining **distances**, **velocities**, **forces**, or other **physical parameters**.

### Finance and Economics

**Equations** frequently arise in **finance** and **economics** to model various scenarios and relationships. **Solving equations** in these contexts can help with **investments**, **interest rates**, **profit margins**, or **economic forecasting calculations**. By **solving equations** like **4(5-x) = 8**, financial analysts and economists can determine unknowns such as pricing, revenue, or **market equilibrium**.

### Optimization and Planning

**Equations** are often used in **optimization problems** where the goal is to find the best possible solution. Researchers and planners can optimize resource allocation, scheduling, production, or logistics by **solving equations**. Equations like **4(5-x) = 8** can represent constraints or objectives that must be satisfied in an **optimization problem**.

### Data Analysis and Modeling

**Equations** are fundamental in **data analysis** and **modeling**. **Solving equations** allows researchers to estimate unknown parameters or variables based on observed data. Analysts can make predictions, draw conclusions, or validate hypotheses by **solving equations** related to statistical models or **regression analysis**.

### Computer Science and Programming

**Equations** play a role in **computer science** and **programming**, particularly in algorithms and numerical methods. **Solving equations** helps solve problems encountered in **algorithm design**, **simulations**, or **optimization routines**. Equations like **4(5-x) = 8** can be part of algorithms or mathematical calculations in various domains, including **machine learning**, **computer graphics**, or **cryptography**.

### Everyday Life

**Solving equations** is not limited to academic or specialized fields. In everyday life, equations are encountered in various contexts, such as **budgeting**, **home improvement**, or **personal finance**. **Solving equations** helps individuals make **informed decisions**, solve practical problems, or plan their activities effectively.

By **solving equations** like **4(5-x) = 8**, we apply fundamental problem-solving skills that find applications in numerous disciplines and situations. Whether in **physics**, **finance**, **optimization**, **data analysis**, **computer science**, or everyday life, **solving equations** is a valuable tool for **decision-making**, understanding relationships, and advancing our understanding of the world around us.

**Exercise **

### Example 1

Solve the equation **4 * (5-x) + 3 = 11**.

### Solution

To solve this equation, we follow similar steps as before:

4 * (5-x) + 3 = 11

20 – 4x + 3 = 11

-4x + 23 = 11

-4x = 11 – 23

-4x = -12

x = (-12) / (-4)

x = 3

So, the **solution** to the equation **4 * (5-x) + 3 = 11** is **x = 3**.

### Example 2

Find the value of x that satisfies the equation **4 * (5-x) = 16**.

Figure-2.

### Solution

We can solve this equation as follows:

4 * (5-x) = 16

20 – 4x = 16

-4x = 16 – 20

-4x = -4

x = (-4) / (-4)

x = 1

Therefore, the value of **x** that satisfies the equation **4 * (5-x) = 16** is **x = 1**.

### Example 3

Determine the solution set for the equation **4 * (5-x) = -8**.

Figure-3.

### Solution

To find the solution set, we proceed as follows:

4 * (5-x) = -8

20 – 4x = -8

-4x = -8 – 20

-4x = -28

x = (-28) / (-4)

x = 7

Hence, the **solution** set for the equation **4 * (5-x) = -8** is **x = 7**.

### Example 4

Solve the equation **4 * (5-x) = 0**.

### Solution

To solve this equation, we proceed as follows:

4 * (5-x) = 0

20 – 4x = 0

-4x = -20

x = (-20) / (-4)

x = 5

So, the **solution** to the equation **4 * (5-x) = 0** is **x = 5**.

### Example 5

Solve the equation **2 * (4-x) – 1 = 20**.

### Solution

To solve the equation **2 * (4-x) – 1 = 20**, we can follow these steps:

Distribute the **2** on the left side of the equation:

2 *** **(4-x) – 1 = 20

8 – 2x – 1 = 20

**Combine** the constants on the left side of the equation:

7 – 2x = 20

To **isolate** the variable term, subtract **7** from both sides of the equation:

7 – 7 – 2x = 20 – 7

-2x = 13

To solve for **x**, divide both sides of the equation by **-2**:

(-2x) / -2 = 13 / -2

x = -6.5

So, the **solution** to the equation **2 * (4-x) – 1 = 20** is **x = -6.5**.

*All images were created with MATLAB.*