Question

What is the difference between the two inequalities? Explain.

X < 3
X ≤ 3

Please help me.

Answer 1

1. For the first inequality, Luz can buy less than 5 computers (since
`x`represents the number of computers and must be less than 5).

2. For the second set of inequalities,
`x` must be greater than -6 and less than 0.

The image shows a mathematical problem with two inequalities:

1.
`\( 70x < 350 \)`

2.
`\( x + 3 < 3 \) and \( x + 3 > -3 \)`

To solve these inequalities step by step, we'll perform the following calculations:

For the first inequality:

`\[ 70x < 350 \]`

1. Divide both sides by 70 to solve for x:

`\[ x < (350)/(70) \]`

For the second set of inequalities:

`\[ x + 3 < 3 \] and \( x + 3 > -3 \)`

1. Subtract 3 from all parts of the compound inequality:

`\[ x < 3 - 3 \]` and
`\( x > -3 - 3 \)`

`\[ x < 0 \]` and
`\( x > -6 \)`

Now let's calculate the values.

Solution for the inequalities:

First inequality:

`\[ 70x < 350 \]`

After dividing both sides by 70, we get:

`\[ x < 5 \]`

Second set of inequalities:

`\[ x + 3 < 3 \]` and
`\( x + 3 > -3 \)`

After subtracting 3 from all parts of the compound inequality, we get:

`\[ x < 0 \]` and
`\( x > -6 \)`

Thus, the solution to the inequalities are:

1. For the first inequality, Luz can buy less than 5 computers (since
`x`represents the number of computers and must be less than 5).

2. For the second set of inequalities,
`x` must be greater than -6 and less than 0.

If we interpret
`x` as the number of items Luz can buy, the negative values don't make sense in a real-world context, as you cannot buy a negative number of items. Therefore, the practical solution for the second inequality is that Luz cannot buy any items since
`x` must be less than 0 and whole numbers (non-negative integers) are required for the count of items.

Answer 2

One includes 3 as a solution, one excludes it.

Explanation:

Think about the difference between the phrase "they were shorter than me" and the phrase "they were no taller than me." In the first one, we're implying that this other person can't be as tall as you; their height has to be less than yours. In the second, we're allowing for the posibility that this person's height matches yours. x < 3 describes that first kind of scenario, while x ≤ 3 describes the second.