If x = 1.011 + 10.11 – 12.101 + 0.1011, then what should be added to x to get…

When a known quantity x must be adjusted by adding some number y so that the total equals a target sum S, the required addend is found using the identity y = S − x. Decimal terms should always be combined by aligning corresponding place values — ones, tenths, hundredths, thousandths, and ten-thousandths — column by column, so that each digit is added or subtracted against its correct place.

1. Add the first two terms: 1.011 + 10.11 = 11.121.

2. Subtract 12.101 from this running total: 11.121 − 12.101 = −0.980.

3. Add 0.1011 to get the value of x: −0.980 + 0.1011 = −0.8789. So x = −0.8789.

4. Apply the addend identity with the target sum S = 1.1: y = S − x = 1.1 − (−0.8789) = 1.1 + 0.8789 = 1.9789.

Check by substitution: x + y = −0.8789 + 1.9789 = 1.1, which matches the required sum exactly, confirming that 1.9789 is the correct addend.