Problem 63 Evaluate $-(-x)$ when: $$ ... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 63

Evaluate $-(-x)$ when: $$ x=\frac{4}{3} $$

Short Answer

Expert verified

$ \frac{4}{3} $

Step by step solution

- Substitute the value of x

First, we need to substitute the given value of $ x $ into the expression $ -(-x) $. The given value of $ x $ is $ \frac{4}{3} $. So, we replace $ x $ in $ -(-x) $ with $ \frac{4}{3} $.

- Simplify the inner negative

Next, simplify the expression inside the parentheses. The inner negative of $ x $ will be $ - \frac{4}{3} $. So the expression becomes $ -(- \frac{4}{3}) $.

- Apply the outer negative

Now, apply the outer negative sign. The negative of a negative will turn into a positive, so $ -(- \frac{4}{3}) $ simplifies to $ \frac{4}{3} $.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

substitution in algebra

Substitution in algebra is a method where you replace a variable with its given value. In this evaluation problem, we see how to work with specific values in place of variables. For instance, we start with the expression $-(-x)$, and the given value of $x$ is $\frac{4}{3}$. By substituting, we replace $x$ with $\frac{4}{3}$, transforming the expression into $-(-\frac{4}{3})$. This foundational step ensures that other operations such as simplification can proceed correctly.

simplifying expressions

Simplifying expressions involves reducing them to their simplest form while maintaining their value. In our problem, we've substituted $x$ and our expression is now $-(-\frac{4}{3})$. First, we simplify inside the parentheses. Here it transforms $-x$ into $-\frac{4}{3}$. Then, we deal with the outermost operations. The outer negative changes the inner expression $-\frac{4}{3}$ to positive, resulting in $\frac{4}{3}$. Simplification helps in making expressions easier to work with and understand.

negative numbers

Negative numbers can initially be tricky, but understanding them is crucial in algebra. A negative sign before a number changes its direction on the number line. When evaluating $-(-x)$ with $x = \frac{4}{3}$, we transform $x$ to its negative form: \-x\ becomes $-\frac{4}{3}$. Then, another negative sign in front, \-(-\frac{4}{3})\, turns the number positive again. This shows a pivotal rule: a double negative equals a positive.

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91影视

Evaluate \(-(-x)\) when: $$ x=\frac{4}{3} $$

Short Answer

Step by step solution

- Substitute the value of x

- Simplify the inner negative

- Apply the outer negative

Key Concepts

substitution in algebra

simplifying expressions

negative numbers

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