Question

6) three times a number increased by four is less than -62

7) the quotient of a number and -5 increased by one is at most 7

8) the quotient of a number and 3 minus two is at least -12

9) the product of -2 and a number minus six is greater than -18

Answer 1

6) 3x + 4 < - 62 x = - 23 ⇒ 3(-23) + 4 < - 62
- 4 - 4 -69 + 4 < - 62
3x < -66 - 65 < - 62
÷ 3 ÷3
x < -22

7) x/-5 + 1 < 7 x = -30 ⇒ -30/-5 + 1 < 7
- 1 -1 6 + 1 < 7
x/-5 < 6 7 < 7
× -5 × -5
x < -30

8) x/3 - 2 > -12 x = -30 ⇒ -30/3 - 2 > -12
x/3 > -10 -10 - 2 > -12
* 3 *3 -12 > -12
x > -30

9) -2x - 6 > -18 x = 5 ⇒ -2(5) - 6 > -18
+6 +6 -10 - 6 > -18
-2x > -12 -16 > -18
÷ -2 ÷ -2
x > 6 ⇒ x < 6
*flip the inequality sign because the divisor is a negative number: This is to make the inequality true.