Question

If w = -4, which inequality is true? Select all the correct answers. A. 2 â€" w < â€"3 B. 5 2w > -7 C. 1 â€" 2w > 13 D. â€"3 â€" 5w < â€"14 E. â€"5 â€" 4w > 10 F. â€"9 â€" 3w < 2.

Answer 1

The inequalities that are  true are 5 +2w > -7 and -3 - 5w < -14

We need to find all the inequality that has a solution of w  = -4

For the inequality 2 - w < -3

-w < -3 - 2

-w < -5

w > 5

• Since -4 is not greater than 5, hence 2 - w < -3 is false

For the inequality 5 +2w > -7

2w > -7 - 5

2w > -12

w > -6

Since -4 is greater than -6 hence 5 +2w > -7 is TRUE

For the inequality 1 - 2w > 13

-2w > 13 - 1

-2w > 12

w < -6

• Since -4 is greater than -6 hence  1 - 2w > 13 is FALSE

For the inequality -3 - 5w < -14

-5w < -14 + 3

-5w < -11

w > 11/5

• Since -4 is less than 11/5 hence   -3 - 5w < -14 is FALSE

For the inequality -5 - 4w > 10

-4w  > 10 + 5

-4w > 15

w < -15/4

w < -3.75

• Since -4 is  less than -3.75 hence   -3 - 5w < -14 is TRUE

For the inequality -9 - 3w < 2

-3w < 2 + 9

-3w < 11

w > -11/3

• Since -4 is  less than -3.67 hence    -9 - 3w < 2 is FALSE

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