Consider the following expressions: 6−14⋅28−214 _______ 34+4⋅2−11 . Which operator can be inserted to make the statement true? Responses = equals ≥ greater-than-or-equal-to < less than >
To determine the missing operator, we need to compare the expressions on both sides of the blank.
On the left side: 6−14⋅28−214 = 6 - (14 * 28) - 214
On the right side: 34 + 4⋅2−11 = 34 + (4 * 2) - 11
Simplifying the expressions:
Left side: 6 - 392 - 214 = -600
Right side: 34 + 8 - 11 = 31
To make the statement true, we need to insert the operator that indicates the left side is less than the right side. So, the correct answer is < (less than).
To determine which operator can be inserted to make the statement true, we need to evaluate both sides of the equation and compare the values.
Let's start by evaluating the left side:
6 - 14 * 28 - 214
To simplify this expression, we should follow the order of operations (PEMDAS/BODMAS). In this case, we should first perform the multiplication:
6 - (14 * 28) - 214
Next, multiply 14 by 28:
6 - 392 - 214
Perform the subtraction:
-600 - 214
Finally, subtract 214 from -600:
-814
Now let's evaluate the right side of the equation:
34 + 4 * 2 - 11
Follow the order of operations:
34 + (4 * 2) - 11
Multiply 4 by 2:
34 + 8 - 11
Perform the addition and subtraction:
42 - 11
Now we can compare the two values:
-814 <?> 31
The left side is -814, and the right side is 31.
To make the statement true, we need to insert the operator that indicates "less than" (<):
-814 < 31
So, the correct operator to insert is < (less than).
To find the missing operator, we need to evaluate the expression on the left side of the blank and the expression on the right side of the blank, and then compare the results.
Let's evaluate the left side expression:
6−14⋅28−214
First, perform the multiplication:
6 - 14 * 28 - 214
= 6 - 392 - 214
Next, perform the subtraction:
= -586 - 214
= -800
Now, let's evaluate the right side expression:
34 + 4⋅2 - 11
First, perform the multiplication:
34 + 4 * 2 - 11
= 34 + 8 - 11
Next, perform the addition and subtraction:
= 42 - 11
= 31
Now, we compare the results:
-800 _____ 31
To make the statement true, we need to find a missing operator that makes -800 equal to or less than 31.
Comparing the two values, we can see that -800 is less than 31. So, the missing operator is < (less than).
Therefore, the correct answer is < (less than).