Did you know?
Did you know that compound inequalities can be solved by writing an inequality that matches the given solution? Take for example the compound inequality -2 ≤ x < 5. To find an inequality that results in this solution, we need at least 4 inverse operations. By adding 2 to both sides, we get 0 ≤ x+2 < 7. Then, subtracting 2 from all sides results in -2 ≤ x < 5.
Now let's have a look at another compound inequality: -1/2 ≥ x or x > 3/5. To find an inequality that yields this solution, we need to perform at least 4 inverse operations. Firstly, we subtract 3/5 from both sides, leading us to -1/2 - 3/5 ≥ x-3/5 or x > 0. By giving a common denominator, this becomes -5/10 - 6/10 ≥ x-3/5 or x > 0. After combining like terms, we have -11/10 ≥ x-3/5 or x > 0. Finally, adding 3/5 to all sides gives us -11/10 + 3/5 ≥ x or x > 0+3/5. Simplifying, we get -13/10 ≥ x or x > 3/5.
Compound inequalities may seem complex, but with the right calculations, you can easily derive the appropriate inequalities to match the given solutions.
