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Linear equations are equations where the variables are raised only to the power of one. They might appear complicated, but they are solvable using straightforward techniques. The first step in solving linear equations is to isolate the variable you are solving for. This usually involves:

• Adding or subtracting terms on both sides to simplify the equation.
• Multiplying or dividing both sides to solve for the variable.

For example, consider the equation \( \frac{x}{-2} + 16 = 11 \). Here, \( x \) is being divided by -2 and added to 16. We start by getting rid of 16 to simplify the equation.
By subtracting 16 from both sides, our equation expedites to \( \frac{x}{-2} = -5 \). Next, remove the division by multiplying both sides by -2, arriving at \( x = 10 \). This shows the value of \( x \) that makes the original equation true.

Algebra is about finding the unknown by using known elements and the operations between them. Operations include addition, subtraction, multiplication, and division. In basic algebra, one must understand how to manipulate equations using these operations.
Solving equations often involves performing opposite operations to isolate variables. For example:

• Addition and subtraction are opposites.
• Multiplication and division are opposites.

In our example, \( \frac{x}{-2} + 16 = 11 \), subtraction is used to counteract addition, and multiplication is used to counteract division to isolate \( x \). Each step simplifies the equation step by step until the unknown is isolated.

Solving inequalities is similar to solving equations, but comes with extra considerations. Inequalities use symbols such as \( > \), \( < \), \( \geq \), and \( \leq \) to denote the relationships between expressions.
In inequalities:

• The goal is to isolate the variable on one side, similar to equations.
• If you multiply or divide by a negative number, remember to reverse the inequality sign.

Reversal is crucial when dealing with negative coefficients, as it changes the direction of the inequality. If an inequality similar to \( \frac{x}{-2} < 5 \) appears, you would multiply both sides by -2, leading to \( x > -10 \) (the sign flips from \( < \) to \( > \)). This ensures that the representation accurately reflects the mathematical relationships in the inequality.