Question

Two questions, is that okay?

1. Solve the inequality, y + 5 ≥ 7
A. y ≤ 2
B. y ≤ 12
C. y ≥ 2
D. y ≥ 12

2. Write an inequality, then solve it. """Fifteen less than a number is at most 6"""
A. x + 15 ≤ 6,,,x ≤ -9
B. x - 15 ≤ 6,,,,x ≤ 21
C. x - 15 ≥ 6,,,x ≥ 21
D. x - 15 ≥ 6,,,x ≥ 16

Answer 1

Answer:

  1.  C.  y ≥ 2

  2.  B.  x -15 ≤ 6   ⇒   x ≤ 21

Step-by-step explanation:

Inequalities are generally solved exactly the same way equations are solved. If you use an operation that changes the ordering of numbers, then you need to adjust the inequality symbol accordingly. Most typically, that situation arises when multiplying or dividing by a negative number. For example, ...

• 1 < 2
• -1 > -2 . . . above equation is multiplied or divided by -1

Operations like adding or subtracting or multiplying by a positive number don't change the order of numbers.

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1. Subtract 5 from both sides of the inequality.

  y +5 -5 ≥ 7 -5

  y ≥ 2 . . . . . . . matches choice C

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2.  "Fifteen less than a number" can be represented by "x -15". The wording "is at most 6" means "is less than or equal to 6". So, the inequality becomes ...

  x -15 ≤ 6

This is solved by adding 15 to both sides.

  x -15 +15 ≤ 6 +15

  x ≤ 21

So, the inequality and answer are ...

  x -15 ≤6 . . . . x ≤ 21 . . . . . . . matches choice B

Answer 2

Answer:

1. Solve the inequality, y + 5 ≥ 7

C. y ≥ 2

2. Write an inequality, then solve it. """Fifteen less than a number is at most 6"""

B. x - 15 ≤ 6,,,,x ≤ 21