Question

Directions: Follow the instructions for the following inequalities.

1. 4<7 Multiply both sides by 7 , then by 6, then by 3, then by 10

2. 11>-2 Add 5 to both sides, then add 3, then add (-4)

3. -4<-2 Subtract 6 from both sides, then 8, and then 2

4. -8<8 Divide both sides by -4, then by -2

5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?

Answer 1

Explanation:

1. Multiplying both sides by positive numbers does not change the direction of the inequality, so the inequality remains true: 28 < 42 < 252 < 1512 < 15120.

2. Adding the same number to both sides of an inequality does not change the direction of the inequality, so the inequality remains true: 16 > 1 > -3 > -7.

3. Subtracting the same number from both sides of an inequality does not change the direction of the inequality, but it changes the values on both sides. The inequality is still true: -10 < -8 < 0.

4. Dividing both sides by negative numbers changes the direction of the inequality, so the inequality sign flips: 2 > -2.

5. The operations in 1, 2, and 3 did not change the truth of the inequality. However, dividing both sides of an inequality by a negative number changes the direction of the inequality. It is important to keep track of the sign of the numbers being multiplied or divided when manipulating inequalities.