91Ó°ÊÓ

Simplifying expressions is an essential skill in algebra. It involves rewriting an expression in a simpler form without changing its value. The first thing to check for is any double negatives or redundant terms. For example, in the equation given:

$$x - \bigg(-\frac{3}{20}\bigg) = -\frac{11}{20}$$

The double negative here (\textasciitilde\textasciitilde) can be simplified to a positive:

$$x + \frac{3}{20} = -\frac{11}{20}.$$

Always look out for such simplification opportunities as they make the next steps easier. Also, combining like terms and using distributive properties where needed are key techniques.

Combining fractions might seem tricky but is straightforward if you follow a few simple rules.

First, ensure that the fractions have a common denominator. In the given exercise, the fractions already have the same denominator (\textasciitilde 20), which makes combining them easier:

$$x = -\frac{11}{20} - \frac{3}{20}.$$

Subtract the numerators while keeping the denominator constant:

$$= -\frac{11 + 3}{20}$$

= -\frac{14}{20}.

Finally, always simplify the fraction if possible. Here, after combining, the numerator and the denominator have a common factor of 2. Dividing both by 2 gives us:

$$-\frac{14}{20} = -\frac{7}{10}.$$

Remember the steps: common denominator, combine numerators, and simplify.

The ultimate goal in solving algebraic equations is to isolate the variable on one side of the equation. Here’s how it’s done in the provided exercise:

Starting with the simplified equation:

$$x + \frac{3}{20} = -\frac{11}{20},.$$

we want to get x by itself. To do this, we subtract \frac{3}{20} from both sides of the equation:

$$x + \frac{3}{20} - \frac{3}{20} = -\frac{11}{20} - \frac{3}{20}.$$

This step ensures that the x term is isolated because \frac{3}{20} - \frac{3}{20} = 0:

$$x= -\frac{11}{20} - ... = -\frac{14}{20}.$$

Lastly, simplify the combined fractions to get the final result:

$$x = -\frac{7}{10}.$$

Isolating the variable typically involves using inverse operations. If a term is added to x, you subtract it. If multiplied, you divide.