Ask a New Question
Menu

Consider the following expressions:

6- ¼ • 28-2 1/2
______ 3/4+4•2-11

Which operator can be inserted to make the statement true?
(1 point)

<
>
=
>

3 answers

To determine which operator can be inserted between the two given expressions to make the statement true, we need to evaluate each expression separately.

First, let's simplify the expression on the left side:

Left Expression: \[ 6 - \frac{1}{4} \times 28 - 2 \frac{1}{2} \]

  • Calculate \(\frac{1}{4} \times 28\): \[ \frac{1}{4} \times 28 = 7 \]
  • Now, substitute into the expression: \[ 6 - 7 - 2 \frac{1}{2} \]
  • Convert \(2 \frac{1}{2}\) to an improper fraction: \[ 2 \frac{1}{2} = \frac{5}{2} = 2.5 \]
  • So now, we have: \[ 6 - 7 - 2.5 = 6 - 7 - 2.5 = -1 - 2.5 = -3.5 \]

Now, let's simplify the expression on the right side:

Right Expression: \[ \frac{3}{4} + 4 \times 2 - 11 \]

  • Calculate \(4 \times 2\): \[ 4 \times 2 = 8 \]
  • Substitute into the expression: \[ \frac{3}{4} + 8 - 11 \]
  • Combine terms: \[ 8 - 11 = -3 \] So now, we have: \[ \frac{3}{4} - 3 \]
  • Convert \(-3\) to a fraction: \[ -3 = -\frac{12}{4} \]
  • Now, we can combine: \[ \frac{3}{4} - \frac{12}{4} = \frac{3 - 12}{4} = \frac{-9}{4} = -2.25 \]

Now we compare the two final results:

  • Left Expression: \(-3.5\)
  • Right Expression: \(-2.25\)

To decide which operator makes the statement true:

\(-3.5\) is less than \(-2.25\).

Thus: \[ -3.5 < -2.25 \]

The correct operator to insert is: \(<\)

So the answer is: <

Which of the following values for b makes the
inequality -32.5 - 66 ≥ 48.5 true?
(1 point)

0-13

• -13.5

• -12.5

• -12

To determine which value of \( b \) makes the inequality \(-32.5 - 66 \geq 48.5\) true, we first simplify the left side of the inequality.

  1. Calculate \(-32.5 - 66\): \[ -32.5 - 66 = -32.5 - 66 = -98.5 \]

Now, we rewrite the inequality: \[ -98.5 \geq 48.5 \] This statement is not true, as \(-98.5\) is much less than \(48.5\).

Since the problem asks for values of \( b \), it seems that the inequality does not depend on \( b \) at this step. The inequality is false regardless of \( b \).

If the question is actually about replacing \( b \) to evaluate a new inequality, we need to clarify the context. However, based on the information provided, the inequality \(-32.5 - 66 \geq 48.5\) is not true for any \( b \) values.

If the intention was to find out which values of \( b \) can satisfy a new inequality, please provide that inequality or clarify how \( b \) would fit into this.

Given the options provided:

  • 0
  • -13
  • -13.5
  • -12.5
  • -12

None of these values would make \(-98.5\) greater than or equal to \(48.5\).

In summary, the inequality \(-98.5 \geq 48.5\) is false, and none of the options for \( b \) would change that. If you are looking for a different inequality to solve or if there’s more context about how \( b \) is used, please let me know!