How do you solve linear inequalities such as: 5x – 2 > 3x + 11

Firstly, I would ask the student if they knew what the first step was. If they did not know, I would suggest that they need to get all the x's on one side of the equation and all the numbers on one side. I would remind them that they can add, subtract, multiply or divide the inequality by any number, as long as they do it to both sides. The student might now realise to add 2 and subtract 3x from both sides. If that is not the case, I would break down the problem into smaller problems and suggest to first try and get all the numbers on one side and ask how they would get rid of the -2 on the left hand side of the inequality. I would then do the same with the values of x. The student will now be left with 2x>13. They should now realise that they need to divide both sides by 2. If they do not realise I will suggest that they need to use division or multiplication to get the "2" on the other side. Lastly the student might get confused by the fact that 13/2 will not give you a whole number. I will remind them that numbers don’t have to be whole and suggest that they look at the nearest even number down (12) and divide that by 2 first and then add 1/2 (0.5) to give them the final result. Lastly I will check that they know which inequality sign is greater and which is smaller.

Throughout this process I will use the pen or text tool on the virtual white board to write down each step as we go along. Finally, I will suggest that the student does one more example of a similar nature (eg. Solve: 2 - 3x > 7x - 3) to make sure they understood the process.