91Ó°ÊÓ

When solving inequalities, the goal is often to isolate the variable on one side of the inequality. This makes it easier to see and compare the value of the variable to the other side. In the inequality \( -x \leq 0 \), we need to isolate the variable x on the left side.
To do this, we must eliminate the negative sign attached to the x. This involves basic arithmetic operations, like addition, subtraction, multiplication, or division. The process of isolating the variable is quite similar to solving algebraic equations, but we must be cautious about how these operations might affect the inequality. Here, we will be multiplying by -1 to get rid of the negative sign.

Reversing the inequality sign is a crucial step when dealing with inequalities. Anytime you multiply or divide by a negative number, you must reverse the direction of the inequality sign to maintain the truth of the statement. This concept can be tricky but is essential for correct solutions.
In our example, \( -x \leq 0 \), we multiply by -1 to isolate x. You must then reverse the inequality sign from \(\leq \) to \(\geq \). So, multiplying both sides of our inequality by -1 changes the inequality to \( x \geq 0 \). This reversal ensures that the inequality correctly represents the value ranges that satisfy the original condition.
This reversal can sometimes be a stumbling block, but always remember to flip the sign whenever dealing with negative multiplications or divisions.

Multiplying or dividing by a negative number is an operation that demands careful attention when solving inequalities. In algebra, this operation is unique because it requires reversing the inequality sign.
For instance, with our problem \[ -x \leq 0 \], multiplying both sides by -1 is necessary to isolate x. However, since we multiplied by a negative number, we must reverse the inequality sign to maintain the correct mathematical relationship. This step transforms our inequality into \[ x \geq 0 \].
Make it a habit to check your steps when performing this action. Multiplying by a negative number changes the entire direction of the inequality, a small but vital detail in algebra.
To summarize: whenever you multiply or divide by a negative number, always remember to flip the inequality sign.