Get the answer to "Determine the solutions Sx for these equations and..."

Hanzikoval1pa

Answered question

2022-03-27

Determine the solutions

S_{x}

for these equations and inequalities

| x - 7 | < - 5

| 2 - 7 x | \leq 12

| 4 - 5 x | \geq 6

Nathanial Carey

Beginner2022-03-28Added 12 answers

| x - 7 | < - 5

Since modulus is always a positive number, for any integer x,

| x - 7 |

can't be less than

- 5

Thus, there is no solution of this inequality over Z
2)

| 2 - 7 x | \leq 12

- 12 \leq 2 - 7 x \leq 12

- 12 \leq 2 - 7 x

7 x \leq 2 + 12

7 x \leq 14

x \leq 2

And

2 - 7 x \leq 12

7 x \geq 2 - 12

7 x \geq - 10

x \geq - \frac{10}{7}

Hence,

- \frac{10}{7} \leq x \leq 2

Now, the integers in between these numbers are:

- 1, 0, 1, 2

And the solution is

S_{x} = [- 1, 0, 1, 2]

German Ferguson

Beginner2022-03-29Added 18 answers

| 4 - 5 x | \geq 6

4 - 5 x \leq - 6

and

4 - 5 x \geq 6

4 - 5 x \leq - 6

5 x \geq 4 + 6

5 x \geq 10

x \geq 2

And

4 - 5 x \geq 6

5 x \leq 4 - 6

5 x \leq - 2

x \leq - \frac{2}{5}

Thus, the integers satisfying

x \geq 2

and

x \leq - \frac{2}{5}

are

- 1, \pm 2, \pm 3, \dots

Therefore, the solutions are:

S_{x} = - 1, \pm 2, \pm 3, \dots

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