# How do you simplify (3/4)abs4 + (-3) – (-1)?

Jul 7, 2015

$\left(\frac{3}{4}\right) \left\mid 4 \right\mid + \left(- 3\right) - \left(- 1\right) = 1$

#### Explanation:

Evaluate the function abs first
Since $\left\mid 4 \right\mid = 4$
The expression becomes
$\textcolor{w h i t e}{\text{XXXX}}$$\left(\frac{3}{4}\right) \left(4\right) + \left(- 3\right) - \left(- 1\right)$

Evaluate the multiplication next
Since $\left(\frac{3}{4}\right) \left(4\right) = 3$
The expression becomes
$\textcolor{w h i t e}{\text{XXXX}}$$3 + \left(- 3\right) - \left(- 1\right)$

Evaluate addition and subtraction starting from the left
Since $3 + \left(- 3\right) = 0$
The expression becomes
$\textcolor{w h i t e}{\text{XXXX}}$$0 - \left(- 1\right)$

Perform the final subtraction
Since $- \left(- 1\right) = + 1$
The expression reduces to
$\textcolor{w h i t e}{\text{XXXX}}$$1$

Jul 11, 2015

$\left(\frac{3}{4}\right) \cdot | 4 | + \left(- 3\right) - \left(- 1\right) = 1$

#### Explanation:

1.) First, let's look at "the absolute value" of $4$

Recall that "the absolute value" of something is something and "the absolute value" of (negative)something is something:

|something| = something
|-something| = something

So, $| 4 | = 4$

2.) So, the $\left(\frac{3}{4}\right) \cdot | 4 |$ part becomes $\left(\frac{3}{4}\right) \cdot 4$ which is $3$

(Those $4$'s cancel out)

3.) Now, we are left with:

$3 + \left(- 3\right) - \left(- 1\right)$

The $+ \left(- 3\right)$ is just $- 3$

because (plus) a (negative)something is (negative)something:

+(-something) = -something

and the $- \left(- 1\right)$ is just $+ 1$

because (minus) a (negative)something is (positive)something:

-(-something) = +something

4.) So, now we have:

$3 - 3 + 1$

$3 - 3$ is $0$ and we are then left with $1$

So, $1$ is our answer (our simplified junk from above)