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The Order of Operations must be used when simplifying a math expression. Put the list below in the correct order.

Multiplication and Division (in order from left to right)
Exponents
Grouping symbols (parentheses, brackets..)
Subtraction and Addition (in order from left to right)

9 answers

The correct order of operations, often remembered by the acronym PEMDAS, is as follows:

  1. Grouping symbols (parentheses, brackets, etc.)
  2. Exponents
  3. Multiplication and Division (from left to right)
  4. Subtraction and Addition (from left to right)

So, the list you've provided should be arranged like this:

  1. Grouping symbols (parentheses, brackets..)
  2. Exponents
  3. Multiplication and Division (in order from left to right)
  4. Subtraction and Addition (in order from left to right)
Simplify by combining like terms: 5a − 8c + b + 3c −9a + 6b

To simplify the expression \(5a - 8c + b + 3c - 9a + 6b\), we will combine like terms.

  1. Identify like terms:

    • For \(a\): \(5a\) and \(-9a\)
    • For \(b\): \(b\) and \(6b\)
    • For \(c\): \(-8c\) and \(3c\)

  2. Combine the like terms:

    • For \(a\): \(5a - 9a = -4a\)
    • For \(b\): \(b + 6b = 7b\)
    • For \(c\): \(-8c + 3c = -5c\)

  3. Write the simplified expression: \[ -4a + 7b - 5c \]

So, the simplified expression is \(-4a + 7b - 5c\).

Select the TWO expressions below that are equivalent to 5(x + 3) - 4
5x-1
5x+15-4
5x-5
5x+11
5x+3-4

To determine which of the expressions are equivalent to \(5(x + 3) - 4\), let's first simplify \(5(x + 3) - 4\):

\[ 5(x + 3) - 4 = 5x + 15 - 4 = 5x + 11 \]

Now we will compare \(5x + 11\) with the given expressions to find the equivalent ones:

  1. Expression: \(5x - 1\)

    • Not equivalent.

  2. Expression: \(5x + 15 - 4\)

    • Equals \(5x + 11\) (equivalent).

  3. Expression: \(5x - 5\)

    • Not equivalent.

  4. Expression: \(5x + 11\)

    • Equivalent.

  5. Expression: \(5x + 3 - 4\)

    • Equals \(5x - 1\) (not equivalent).

The two expressions that are equivalent to \(5(x + 3) - 4\) are:

  • \(5x + 15 - 4\)
  • \(5x + 11\)
are you 100%%%!!!!!!!!!! sureeee!!!!!!!

Yes, I am certain! Let’s double-check the calculations to ensure clarity:

We started with the expression \(5(x + 3) - 4\):

  1. Distributing \(5\) in \(5(x + 3)\): \[ 5(x) + 5(3) = 5x + 15 \]

  2. Then, we subtract \(4\): \[ 5x + 15 - 4 = 5x + 11 \]

So the simplified version of \(5(x + 3) - 4\) is indeed \(5x + 11\).

Now comparing this result \(5x + 11\) with the options provided:

  1. \(5x - 1\): Not equivalent to \(5x + 11\)
  2. \(5x + 15 - 4\): This simplifies to \(5x + 11\) (equivalent)
  3. \(5x - 5\): Not equivalent
  4. \(5x + 11\): Equivalent
  5. \(5x + 3 - 4\): This simplifies to \(5x - 1\) (not equivalent)

Thus, the two equivalent expressions are:

  • \(5x + 15 - 4\)
  • \(5x + 11\)

I confirm that the initial conclusion was correct! If you have any more questions or need further clarification, feel free to ask!

Factor the algebraic expression: 5m - 15

____(m-3)

5
15
-5
3

To factor the expression \(5m - 15\), we can look for a common factor.

  1. Identify the common factor: The terms \(5m\) and \(-15\) both have a common factor of \(5\).

  2. Factor out the common factor: \[ 5m - 15 = 5(m - 3) \]

So, the expression \(5m - 15\) factors as \(5(m - 3)\).

Now, the blank in your question should be filled with \(5\). Thus, the completed expression is:

\[ 5(m - 3) \]

So the correct answer is 5.