91Ó°ÊÓ

When solving an inequality, the first goal is to isolate the variable. This helps us simplify and find the value range for the variable. In the inequality:\[2x + 5 < 9\]we want to isolate the term with the variable, which is '2x'. To do this, we need to remove the constant term on the same side, which is +5. This process involves performing the same operation on both sides of the inequality.
To isolate '2x', we subtract 5 from both sides:\[2x + 5 - 5 < 9 - 5\]By doing this, we effectively cancel out the +5 on the left side, leaving us with:\[2x < 4\]Now, '2x' is isolated, and we can proceed to the next step.

After isolating the variable term, the next step is to simplify the inequality. Simplification makes the equation easier to work with. From the previous step, we have:\[2x < 4\]This inequality is already in a simpler form, so our main job here is to ensure it remains an inequality in its true form. No additional steps are required in this case as it is already straightforward. Now, we need to solve for 'x'.

To solve for the variable, we need to isolate 'x' completely. Since '2x' means 2 times 'x', we divide both sides of the inequality by 2. This helps us find the value of 'x'. We perform the division on both sides to maintain the balance, just like we did with subtraction.
Starting from:\[2x < 4\]We divide both sides by 2:\[\frac{2x}{2} < \frac{4}{2}\]This simplifies to:\[x < 2\]Thus, the solution to our inequality is:\[x < 2\]This means that 'x' can be any value less than 2. By carefully following these steps—isolating the variable, simplifying the inequality, and dividing both sides—we can successfully solve inequalities and understand the range of possible values for the variable.