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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?

Sagot :

semsee45

Answer:

1. 5050 < 8820

2. 15 > 6

3. -20 , -18

4. -1 < 1

Step-by-step explanation:

1. 4 < 7

multiply both sides by 7:  4 x 7 < 7 x 7 = 28 < 49

then multiply both sides by 6: 28 x 6 < 49 x 6 = 168 < 294

then multiply both sides by 3: 168 x 3 < 294 x 3 = 505 < 882

then multiply both sides by 10:  505 x 10 < 882 x 10 = 5050 < 8820

Did not affect the inequality sign

2. 11 > 2

Add 5 to both sides:  11 + 5 > 2 + 5 = 16 > 7

then add 3 to both sides:  16 + 3 > 7 + 3 = 19 > 10

then add -4 to both sides: 19 - 4 > 10 - 4 = 15 > 6

Did not affect the inequality sign

3. -4 < -2

Subtract 6 from both sides: - 4 - 6 < - 2 - 6 = -10 < -8

then subtract 8 from both sides: -10 - 8 < -8 - 8 = -18 < -16

then subtract 2 from both sides:  -18 - 2 < -16 - 2 = -20 , -18

Did not affect the inequality sign

4. -8 < 8

Divide both sides by -4: -8 ÷ -4 < 8 ÷ -4 = 2 > -2

then divide both sides by -2:  2 ÷ -2 > -2 ÷ -2 = -1 < 1

Did affect the inequality sign throughout the operations, as when dividing by a negative number, flip the sign

5.

  • Adding or subtracting the same quantity from both sides of an inequality leaves the inequality symbol unchanged.
  • Multiplying or dividing both sides by a positive number leaves the inequality symbol unchanged.
  • Multiplying or dividing both sides by a negative number reverses the inequality.  This means < changes to > (and vice versa)
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