In mathematics, solving inequalities is a process of finding the values of the variables that make the inequality true. This is a difficult concept for many students to understand, as it requires knowledge of algebra and the ability to think logically. In this article, we will explore how to solve the inequality 2(4+2x)≥5x+5.

## Understanding Solving Inequalities

Solving inequalities requires a student to use the same skills used to solve equations. This process begins with isolating the variable by using inverse operations, such as addition, subtraction, multiplication, and division. Once the variable is isolated, the student must determine the range of values that make the inequality true. This process is done by plugging in different values for the variable and seeing which values make the inequality true.

## Solving 2(4+2x)≥5x+5

To solve 2(4+2x)≥5x+5, we must isolate the variable by using inverse operations. We can start by subtracting 5x from both sides of the equation. This gives us 2(4+2x)-5x ≥ 5. Next, we can divide both sides of the equation by 2. This gives us 4+2x ≥ 5/2. Finally, we can subtract 4 from both sides of the equation. This gives us 2x ≥ 1/2.

From here, we can determine the range of values that make the inequality true. If we plug in a value of x that is less than or equal to -2, the inequality will be true. This means that x≤−2. If we plug in a value of x that is greater than or equal to -2, the inequality will also be true. This means that x≥−2.

Finally, if we plug in a value of x that is less than or equal to 3, the inequality will be true. This means that x≤3. If we plug in a value of x that is greater than or equal to 3, the inequality will not be true. This means that x≥3.

Solving inequalities is a difficult process that requires a student to understand algebra and think logically. In this article, we explored how to solve the inequality 2(4+2x)≥5x+5. We determined that the range of values that make the inequality true are x≤−2, x≥−2, x≤3, and