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BIG IDEAS MATH

#1 1
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0x-b-3-0
00>b-x+3
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B.E.S.T. TEST PREP Which of the following inequalities are equivalent to the inequality
x-b<3, where b is a constant? Select all that apply.

x-b-3<0
x<3-b
0>b-x+3
-3

Answer 1

To determine which inequalities are equivalent to the inequality x - b < 3, let's analyze each option:

x - b - 3 < 0: This inequality is equivalent to x - b < 3 because if you add 3 to both sides of x - b - 3 < 0, you get x - b < 3. So, it is equivalent.
x < 3 - b: This inequality is also equivalent to x - b < 3. You can rearrange it to x - b < 3 by adding b to both sides, giving x < 3 - b + b, which simplifies to x < 3.
0 > b - x + 3: This inequality is not equivalent to x - b < 3. It is essentially the reverse of the original inequality. It's saying that b - x + 3 is negative, which is different from x - b being less than 3.
-3: This is not an inequality but a constant value.
So, the inequalities that are equivalent to x - b < 3 are:

x - b - 3 < 0
x < 3 - b
These two inequalities represent the same relationship as x - b < 3, where b is a constant.

Answer 2

To determine which of the given inequalities are equivalent to the inequality x - b < 3, where b is a constant, we can analyze each option:

1. x - b - 3 < 0:

This inequality is equivalent to x - b < 3 because if you add 3 to both sides, you get x - b < 3.

2. x < 3 - b:

This inequality is also equivalent to x - b < 3 because you can add b to both sides, giving x - b < 3.

3. 0 > b - x + 3:

This inequality is not equivalent to x - b < 3. It's the reverse of x - b > -3, which is not the same as x - b < 3.

4. -3:

This is not an inequality; it's just a constant value.

So, the inequalities that are equivalent to x - b < 3 are:

1. x - b - 3 < 0

2. x < 3 - b