Answer:
Rewritten: [tex]\frac{37}{5}p+\frac{13}{5} =\frac{83}{10} p+\frac{53}{10}[/tex]
Solved: [tex]p=-3[/tex]
Step-by-step explanation:
A way you could rewrite the equation without decimals is with fractions.
- 7.4 is equal to [tex]7\frac{4}{10}[/tex] or [tex]\frac{74}{10}[/tex] which simplifies to [tex]\frac{37}{5}[/tex]
- 2.6 is equal to [tex]2\frac{6}{10}[/tex] or [tex]\frac{26}{10}[/tex] which simplifies to [tex]\frac{13}{5}[/tex]
- 8.3 is equal to [tex]8\frac{3}{10}[/tex] or [tex]\frac{83}{10}[/tex]
- and 5.3 is equal to [tex]5\frac{3}{10}[/tex] or [tex]\frac{53}{10}[/tex]
So the rewritten equation would look like [tex]\frac{37}{5}p+\frac{13}{5} =\frac{83}{10} p+\frac{53}{10}[/tex] .
In order to solve it, we want to get all of the variables, in this case "p," on one side of the equation.
- It will also help to have all the denominators be the same number. Since [tex]\frac{83}{10}[/tex] and [tex]\frac{53}{10}[/tex] cannot be simplified any further, we multiply [tex]\frac{37}{5}[/tex] and [tex]\frac{13}{5}[/tex] by [tex]\frac{2}{2}[/tex] so they also have a denominator of 10.
To solve, we add [tex]\frac{26}{10}[/tex] to the right side and subtract [tex]\frac{83}{10} p[/tex] from the right side:
- The equation now looks like this: [tex]\frac{74}{10}p-\frac{83}{10} p=\frac{53}{10}-\frac{26}{10}[/tex]
Now we can factor out the "p" from the left side:
- [tex]p(\frac{74}{10}-\frac{83}{10})=\frac{53}{10}-\frac{26}{10}[/tex]
We can simplify [tex]\frac{74}{10}-\frac{83}{10}[/tex] and [tex]\frac{53}{10}-\frac{26}{10}[/tex] to [tex]\frac{74-83}{10}=-\frac{9}{10}[/tex] and[tex]\frac{53-26}{10}=\frac{27}{10}[/tex]:
- [tex]p(-\frac{9}{10})=\frac{27}{10}[/tex]
Then we would divide the right side by [tex]-\frac{9}{10}[/tex]:
- [tex]p=\frac{\frac{27}{10}}{-\frac{9}{10}}[/tex]
Next we multiply the numerator by the reciprocal of the denominator:
- [tex]p=\frac{27}{10}(-\frac{10}{9} )[/tex]
Then we multiply:
- [tex]p=-\frac{270}{90}[/tex]
And finally, simplify:
