Practice Problems

1. $-{\displaystyle \frac{9}{8}}+\text{g}=-{\displaystyle \frac{3}{8}}$ (
   Solution

   x

   Solution: ${\displaystyle \frac{3}{4}}$
   Details:
   In this example, you are solving for the variable g. The only operation involved between g and other numbers is addition. Solve this the same way you solve equations with integers. Unravel the equation using the order of operations backward.
   
   Step 1: Do the inverse of any addition or subtraction.
   
   On the left-hand side of the equal sign $-{\displaystyle \frac{9}{8}}$ is being added to g. Remove this by adding the inverse to both sides of the equation.
   
   Add $+{\displaystyle \frac{9}{8}}$ to both sides.
    
   The left side of the equation:
   $-{\displaystyle \frac{9}{8}}+{\displaystyle \frac{9}{8}}=0$ leaving just the variable g.
   
   The right side of the equation:
   
   Since both of these fractions have the same denominator you can add the numerators.
   
   $-{\displaystyle \frac{3}{8}}+{\displaystyle \frac{9}{8}}={\displaystyle \frac{6}{8}}$
    
   Normally this would be the end of your work since you isolated the solution for variable g, but in this case, you can still simplify the fraction.
   
   6 and 8 both have 2 as a common factor.
   
   $6=(2)(3)$
   
   $8=(2)(4)$
   
   Divide out the 2’s leaving just ${\displaystyle \frac{3}{4}}$.
   
   $\text{g}={\displaystyle \frac{6}{8}}={\displaystyle \frac{\left(2\right)\left(3\right)}{\left(2\right)\left(4\right)}}={\displaystyle \frac{\cancel{\left(2\right)}\left(3\right)}{\cancel{\left(2\right)}\left(4\right)}}={\displaystyle \frac{3}{4}}$
   
   The final solution is: $\text{g}={\displaystyle \frac{3}{4}}$.
   )
2. $\text{r}+{\displaystyle \frac{1}{4}}=-1$ (
   Solution

   x

   Solution: $-{\displaystyle \frac{5}{4}}$
   )
3. $\text{x}+{\displaystyle \frac{5}{9}}={\displaystyle \frac{1}{3}}$ (
   Solution

   x

   Solution: $-{\displaystyle \frac{2}{9}}$
   Details:
   In this example, you need to get the variable x all alone. To do this, add the inverse of ${\displaystyle \frac{5}{9}}$ to both sides of the equation.
   
   Add $-{\displaystyle \frac{5}{9}}$ to both sides.
    
   The left side of the equation:
   
   Positive ${\displaystyle \frac{5}{9}}$ plus negative ${\displaystyle \frac{5}{9}}$ equals 0. This leaves just the variable x by itself.
    
   The right side of the equation:
   
   In order to add ${\displaystyle \frac{1}{3}}+-{\displaystyle \frac{5}{9}}$ you need to first get common denominators.
   
   9 is a multiple of 3, so the least common multiple is 9.
   
   Multiply ${\displaystyle \frac{1}{3}}$ by 1 in the form of ${\displaystyle \frac{3}{3}}$ to change its denominator to 9.
   
   $\text{X}=\left({\displaystyle \frac{1}{3}}\right)\left({\displaystyle \frac{3}{3}}\right)+-{\displaystyle \frac{5}{9}}$
   
   $\text{X}={\displaystyle \frac{1\cdot 3}{3\cdot 3}}+-{\displaystyle \frac{5}{9}}$
   
   $\text{X}={\displaystyle \frac{3}{9}}+-{\displaystyle \frac{5}{9}}$
   
   Now that the fractions have the same denominator, you can add the numerators.
   
   $3+-5=-2$
   
   $\text{X}={\displaystyle \frac{3}{9}}+-{\displaystyle \frac{5}{9}}$
   
   $\text{X}={\displaystyle \frac{3+-5}{9}}$
   
   $\text{X}={\displaystyle \frac{-2}{9}}$
   
   The final solution is: $\text{X}=-{\displaystyle \frac{2}{9}}$.
   )
4. $-3+\text{g}={\displaystyle \frac{5}{2}}$ (
   Solution

   x

   Solution: ${\displaystyle \frac{11}{2}}$
   )
5. $-4=\text{j}+{\displaystyle \frac{4}{3}}$ (
   Video Solution

   x

   Solution: ${\displaystyle \frac{-16}{3}}$
   Details:
   

   
   
   ) | Transcript)
6. ${\displaystyle \frac{7}{6}}=\text{A}-{\displaystyle \frac{1}{2}}$ (
   Solution

   x

   Solution: ${\displaystyle \frac{5}{3}}$
   )
7. ${\displaystyle \frac{-9}{8}}={\displaystyle \frac{-3}{4}}+\text{a}$ (
   Video Solution

   x

   Solution: ${\displaystyle \frac{-3}{8}}$
   Details:
   

   
   
   | Transcript)