RTCNTC said:|[3(x - 2)/4] + 4(x - 1)/3| ≤ 2
Can I use the following theorem?
If a > 0, then | u | < a if and only if -a < u < a
RTCNTC said:|[3(x - 2)/4] + 4(x - 1)/3| ≤ 2
Can I use the following theorem?
If a > 0, then | u | < a if and only if -a < u < a
When we talk about solving an inequality, we are referring to finding the values of the variable that make the inequality true. This is similar to solving an equation, but instead of finding a single answer, we are finding a range of values that satisfy the inequality.
There are three main types of inequalities: greater than (>), less than (<), and not equal to (≠). Within these types, there are also variations such as greater than or equal to (≥) and less than or equal to (≤).
To solve an inequality with variables on both sides, you will need to first isolate the variable on one side of the inequality sign. This can be done by using inverse operations (e.g. adding, subtracting, multiplying, or dividing) to move the terms to the other side. Once the variable is isolated, you can solve for it as you would a normal equation.
Yes, you can graph an inequality on a coordinate plane. The graph will show the range of values that satisfy the inequality. If the inequality has a greater than or less than sign, the line on the graph will be dashed to indicate that the values on the line itself are not included in the solution. If the inequality has a greater than or equal to or less than or equal to sign, the line on the graph will be solid to indicate that the values on the line are included in the solution.
To check if a solution to an inequality is correct, you can plug the value into the inequality and see if it makes the statement true. If it does, then the solution is correct. If it does not, then the solution is incorrect. It is always a good idea to check your solutions to ensure that you have not made any errors during the solving process.