Solve for c: c + 1.2 = -1 \frac{2}{5}

Okay, let's solve the equation for 'c'. First, we need to convert the mixed number $$-1\frac{2}{5}$$ into an improper fraction. To do this, we multiply the whole number part (1) by the denominator (5) and add the numerator (2). This gives us $$(1 \times 5) + 2 = 7$$. Since the original number was negative, the improper fraction is $$-\frac{7}{5}$$. So our equation now looks like this: $$c + 1.2 = -\frac{7}{5}$$ Next, let's convert the decimal 1.2 into a fraction. 1.2 is the same as $$\frac{12}{10}$$. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, $$\frac{12}{10}$$ simplifies to $$\frac{6}{5}$$. Now our equation is: $$c + \frac{6}{5} = -\frac{7}{5}$$ To isolate 'c', we need to subtract $$\frac{6}{5}$$ from both sides of the equation: $$c = -\frac{7}{5} - \frac{6}{5}$$ Since we are subtracting fractions with the same denominator, we can simply subtract the numerators: $$c = \frac{-7 - 6}{5}$$ $$c = \frac{-13}{5}$$ So, $$c = -\frac{13}{5}$$. Now, let's convert this improper fraction back into a mixed number. We divide 13 by 5, which gives us 2 with a remainder of 3. Therefore, $$-\frac{13}{5}$$ is equal to $$-2\frac{3}{5}$$. Finally, let's convert the fraction $$-2\frac{3}{5}$$ to a decimal. $$-\frac{3}{5}$$ as decimal is equal to -0.6. Add the whole number and we get -2.6 Answer: c = -2.6