Answer
which phrases can be represented by the algebraic expression x + 14? select three options.

1. the quotient of a number and 14
2. a number plus 14
3. fourteen less than a number
4. fourteen more than a number
5. a number increased by 14

The phrases can be represented by the algebraic expression x + 14 are:

Option 2: A number plus 14

Option 4: Fourteen more than a number

Option 5: A number increased by 14

Solution:

Given that we have to find the phrases represented by algebraic expression

Given expression is:

x + 14

This expression means that "x" is increased by 14 or 14 is added to x

Let us check the options one by one

The quotient of a number and 14

So this expression is wrong, since it involves quotient which is not related to given expression

A number plus 14

Writing it mathematically,

number + 14

If the number be "x", then we get x + 14

So this option is correct

Fourteen less than a number

Writing it mathematically,

number - 14

If the number be "x", then we get x - 14

So this Option is wrong

Fourteen more than a number

Here, "more than" means addition

Writing it mathematically,

14 + number

If the number be "x", then we get 14 + x which is same as x + 14

So this option is correct

A number increased by 14

Here, "increased by" means addition

Writing it mathematically,

number + 14

If the number be "x", then we get x + 14

So this option is correct

Thus correct options are option 2, 4, 5