Consider the following expressions: −6+3⋅5 ______ 16−−√+32÷8 . Which operator can be inserted to make the statement true?

Answer 1

Let's evaluate both sides of the expression given:

1. For the left side: \(-6 + 3 \cdot 5\)

   First, we perform the multiplication: \[ 3 \cdot 5 = 15 \]

   Now, we add: \[ -6 + 15 = 9 \]

2. For the right side: \(16 - \sqrt{16} + 32 \div 8\)

   First, let's calculate \(\sqrt{16}\): \[ \sqrt{16} = 4 \]

   Next, calculate \(32 \div 8\): \[ 32 \div 8 = 4 \]

   Now we substitute back into the expression: \[ 16 - 4 + 4 \]

   Now we perform the calculations from left to right: \[ 16 - 4 = 12 \] \[ 12 + 4 = 16 \]

So we now have: \[ 9 \quad ___ \quad 16 \]

To determine which operator can be inserted into the blank to make the statement true, we need to compare \(9\) and \(16\). The possible operators are \(<\), \(>\), and \(=\).

Since \(9 < 16\), we can use the less-than operator:

Thus, the correct operator to insert is \(<\).

Final expression: \(-6 + 3 \cdot 5 < 16 - \sqrt{16} + 32 \div 8\) is true.