Question

Jack solved the following inequality incorrectly, but he cannot figure out where he went wrong. Find Jack's mistake(s) and write a note to him to help him solve the inequality correctly.

Jack's Solution and Work:
1-2x < 11
2x < 10
x < 5

Answer 1

Jack made a mistake when solving the inequality 1-2x < 11. The correct solution is x > -5.

Step-by-step explanation:

Jack made a mistake when solving the inequality. Let's go through the correct steps:

1. Start with the original inequality: 1-2x < 11
2. Add 2x to both sides: 1-2x+2x < 11+2x
3. Simplify: 1 < 11+2x
4. Subtract 11 from both sides: 1-11 < 11+2x-11
5. Simplify: -10 < 2x
6. Divide by 2: -10/2 < 2x/2
7. Simplify: -5 < x

The correct solution to the inequality is x > -5. Jack mistakenly wrote x < 5 as the solution. Remember that when you multiply or divide both sides of an inequality by a negative number, you need to reverse the direction of the inequality sign.