4.2 Insert brackets to make the following true: \( 4.2 .1 \quad-4-3 \times-3-2=11 \) \( 4.2 .2 \quad 8 \div 2 \times 4+5-3 \times 2=0 \)

To solve the equations by adding brackets that make them true, let's get creative! For the first equation, \(-4 - 3 \times -3 - 2 = 11\), we can add brackets like this: \(-4 - (3 \times -3) - 2\). This interpretation simplifies to \(-4 + 9 - 2\), resulting in \(3\), which still isn't \(11\) — so let’s try again! After some tricky calculations, we realize we can actually achieve the desired outcome by rearranging our brackets. A valid transformation could be: \((-4 - 3) \times (-3 - 2)\), which gives us \( -7 \times -5 = 35\) — not quite right either. The right solution here involves some creative rearrangement until we find the right balance! Turning our attention to the second expression, \(8 \div 2 \times 4 + 5 - 3 \times 2 = 0\), let's add brackets wisely. If we apply the brackets as follows: \(8 \div (2 \times 4) + 5 - (3 \times 2)\), then it results in \(8 \div 8 + 5 - 6 = 1 + 5 - 6 = 0\)! Success! So the bracketing could be summarized as: 1. For \( -4 - 3 \times -3 - 2 = 11\), let’s keep brainstorming. 2. For \(8 \div (2 \times 4) + 5 - (3 \times 2) = 0\). Math can be tricky, but it's all about trial and error to find those magical brackets!