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Check all of the expressions that are equal to the one below.

(7 - 11) x (5)

Group of answer choices

(5) x 7 + (5) x (-11)

(5) x 7 - (5) x 11

-(-7 + 11) x (5)

(7 + 11) x (5)

5 answers

Let's evaluate the expression \( (7 - 11) \times (5) \):

\[ (7 - 11) = -4 \]

Thus,

\[ (7 - 11) \times (5) = -4 \times 5 = -20 \]

Now, let's check the other expressions to see which ones equal \(-20\).

  1. Expression 1: \( (5) \times 7 + (5) \times (-11) \)

    \[ (5 \times 7) + (5 \times -11) = 35 - 55 = -20 \]

    So, this expression equals \(-20\).

  2. Expression 2: \( (5) \times 7 - (5) \times 11 \)

    \[ (5 \times 7) - (5 \times 11) = 35 - 55 = -20 \]

    So, this expression also equals \(-20\).

  3. Expression 3: \( -(-7 + 11) \times (5) \)

    \[ -(-7 + 11) = -4 \]

    So,

    \[ -(-7 + 11) \times 5 = -4 \times 5 = -20 \]

    This expression also equals \(-20\).

  4. Expression 4: \( (7 + 11) \times (5) \)

    \[ (7 + 11) = 18 \]

    Thus,

    \[ (7 + 11) \times (5) = 18 \times 5 = 90 \]

    This expression does not equal \(-20\).

Summary

The expressions that are equal to \( (7 - 11) \times (5) \) are:

  • \( (5) \times 7 + (5) \times (-11) \)
  • \( (5) \times 7 - (5) \times 11 \)
  • \( -(-7 + 11) \times (5) \)

So, the correct answers are:

  • (5) x 7 + (5) x (-11)
  • (5) x 7 - (5) x 11
  • -(-7 + 11) x (5)
which ones

first
second
third
or fourth

Here’s the correct identification of the expressions based on your provided choices:

  1. First: \( (5) \times 7 + (5) \times (-11) \)
    This is equal to \(-20\). (Correct)

  2. Second: \( (5) \times 7 - (5) \times 11 \)
    This is equal to \(-20\). (Correct)

  3. Third: \( -(-7 + 11) \times (5) \)
    This is equal to \(-20\). (Correct)

  4. Fourth: \( (7 + 11) \times (5) \)
    This is not equal to \(-20\). (Incorrect)

Summary of Correct Expressions:

  • First: Correct
  • Second: Correct
  • Third: Correct
  • Fourth: Incorrect

So, the expressions that are equal to the original expression are the first, second, and third options.

The absolute value of a number is

The absolute value of a number is a measure of its distance from zero on the number line, regardless of its direction. It is always a non-negative value.

Mathematically, the absolute value of a number \( x \) is denoted as \( |x| \) and is defined as follows:

  • If \( x \geq 0 \), then \( |x| = x \)
  • If \( x < 0 \), then \( |x| = -x \) (which is positive)

For example:

  • \( |5| = 5 \)
  • \( |-5| = 5 \)
  • \( |0| = 0 \)

In summary, the absolute value represents the "size" or "magnitude" of a number without regard to its sign.