Questions: Simplify the inequality to determine whether it is true or false. 2[2+2(4+4)] ≤ 10 Is the statement true or false? True False

Solution Steps

To determine whether the inequality is true or false, we need to simplify the left side of the inequality using the order of operations (parentheses, exponents, multiplication and division, addition and subtraction). Once simplified, we compare the result to the right side of the inequality to see if it holds true.

We start with the inequality \( 2[2 + 2(4 + 4)] \leq 10 \). First, we simplify the expression inside the brackets: \[ 4 + 4 = 8 \] Now substituting back, we have: \[ 2[2 + 2 \cdot 8] \] Next, we calculate \( 2 \cdot 8 \): \[ 2 \cdot 8 = 16 \] Now substituting this value back, we get: \[ 2[2 + 16] = 2[18] \] Finally, we calculate \( 2 \cdot 18 \): \[ 2 \cdot 18 = 36 \]

Now we compare the simplified left side \( 36 \) with the right side \( 10 \): \[ 36 \leq 10 \] This statement is false.

Final Answer