Question

Consider the following statement:

8⋅3+2⋅6 ______ 60÷5⋅3
.

Which operator can be inserted to make the statement true?

(1 point)

Answer 1

Which of the following values of x makes the equation 2x−−√+13=27
true?(1 point)
Responses

16
16

25
25

9
9

49

Answer 2

To determine which operator can be inserted to make the statement true, we need to evaluate both sides of the equation step by step.

First, let's calculate the left-hand side (LHS):

\[
8 \cdot 3 + 2 \cdot 6
\]
Calculating this:
\[
8 \cdot 3 = 24
\]
\[
2 \cdot 6 = 12
\]
So,
\[
LHS = 24 + 12 = 36
\]

Now, let's calculate the right-hand side (RHS):

\[
60 \div 5 \cdot 3
\]
Calculating this:
\[
60 \div 5 = 12
\]
Then:
\[
12 \cdot 3 = 36
\]
So,
\[
RHS = 36
\]

Now we have:
\[
36 \, \_ \, 36
\]
We need to determine which operator can go in the blank space (underscore).

The operators we can use are:
- = (equals)
- < (less than)
- > (greater than)
- ≠ (not equal)

Since LHS = RHS equals both sides (36 = 36), we can insert the equals sign “=”.

The complete statement would be:
\[
8 \cdot 3 + 2 \cdot 6 = 60 \div 5 \cdot 3
\]

Thus, the operator to insert is "=".

Answer 3

To solve the equation \( \sqrt{2x} + 13 = 27 \), we first isolate the square root term.

1. Subtract 13 from both sides:
\[
\sqrt{2x} = 27 - 13
\]
\[
\sqrt{2x} = 14
\]

2. Next, square both sides to eliminate the square root:
\[
2x = 14^2
\]
\[
2x = 196
\]

3. Now, divide both sides by 2 to solve for \( x \):
\[
x = \frac{196}{2}
\]
\[
x = 98
\]

Now, let's check which of the given options (16, 25, 9, 49) makes this equation true.
Since none of the provided responses (16, 25, 9, 49) equals 98, none of them are correct.

If you need to check each one:
- For \( x = 16 \):
\[
\sqrt{2(16)} + 13 = \sqrt{32} + 13 \neq 27
\]
- For \( x = 25 \):
\[
\sqrt{2(25)} + 13 = \sqrt{50} + 13 \neq 27
\]
- For \( x = 9 \):
\[
\sqrt{2(9)} + 13 = \sqrt{18} + 13 \neq 27
\]
- For \( x = 49 \):
\[
\sqrt{2(49)} + 13 = \sqrt{98} + 13 \neq 27
\]

As none of the provided values satisfy the equation, it seems there is an inconsistency between the equation and the provided options. The value that makes the equation true is \( x = 98 \), which is not among the choices.