Question

The number 0 is a solution to which of the following inequalities? Select all that apply.

x - 5 ≤ -3
x ≥ 0
x + 11 > 12
4x ≤ 12
4x < 0

Answer 1

0 is a solution to the inequalities x - 5 ≤ -3 and 4x ≤ 12. While it's not a solution to 4x < 0, 0 is the boundary point where the inequality changes.

Step-by-step explanation:

The number 0 is a solution to the following inequalities: x - 5 ≤ -3, 4x ≤ 12, and 4x < 0. To determine this, substitute x with 0 in each inequality and simplify:

0 - 5 ≤ -3 which simplifies to -5 ≤ -3, and this is true.

4×0 ≤ 12 simplifies to 0 ≤ 12, and this is also true.

4×0 < 0 simplifies to 0 < 0, which is not true; however, 0 is the boundary point for this inequality where the inequality changes from being true to false.

Answer 2

the number
`\( 0 \)` is a solution to the following inequalities:

-
`\( x - 5 \leq -3 \)`

-
`\( x \geq 0 \)`

-
`\( 4x \leq 12 \)`

Therefore, option A,B and D are correct

Let's evaluate each inequality by substituting \( x = 0 \) to see if the inequality holds true.

1.
`\( x - 5 \leq -3 \)`

Substituting
`\( x = 0 \)`:

`\( 0 - 5 \leq -3 \)`

`\( -5 \leq -3 \)`

This inequality is true because
`\(-5\)` is indeed less than or equal to
`\(-3\)`. Therefore,
`\( x = 0 \)` is a solution to this inequality.

2.
`\( x \geq 0 \)`

Substituting
`\( x = 0 \)`:

`\( 0 \geq 0 \)`

This inequality is also true because
`\( 0 \)` is equal to
`\( 0 \)`. Therefore,
`\( x = 0 \)` is a solution to this inequality.

3.
`\( x + 11 > 12 \)`

Substituting
`\( x = 0 \)`:

`\( 0 + 11 > 12 \)`

`\( 11 > 12 \)`

This inequality is false because \( 11 \) is not greater than \( 12 \). Therefore, \( x = 0 \) is not a solution to this inequality.

4.
`\( 4x \leq 12 \)`

Substituting
`\( x = 0 \)`:

`\( 4 * 0 \leq 12 \)`

`\( 0 \leq 12 \)`

This inequality is true because
`\( 0 \)` is indeed less than or equal to
`\( 12 \)`. Therefore,
`\( x = 0 \)` is a solution to this inequality.

5.
`\( 4x < 0 \)`

Substituting
`\( x = 0 \)`:

`\( 4 * 0 < 0 \)`

`\( 0 < 0 \)`

This inequality is false because
`\( 0 \)` is not less than
`\( 0 \)`. Therefore,
`\( x = 0 \)` is not a solution to this inequality.

In conclusion, the number
`\( 0 \)` is a solution to the following inequalities:

-
`\( x - 5 \leq -3 \)`

-
`\( x \geq 0 \)`

-
`\( 4x \leq 12 \)`