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In Solve Simple Interest Applications , we used the formula to calculate simple interest, where is interest, is principal, is rate as a decimal, and is time in years.
Solve the formula to find the principal,
I = $5600, r = 4%, t = 7 years | in general | |
Write the forumla. | ||
Substitute any given values. | ||
Multiply r ⋅ t . | ||
Divide to isolate P . | ||
Simplify. | ||
State the answer. | The principal is $20,000. |
Later in this class, and in future algebra classes, you’ll encounter equations that relate two variables, usually and You might be given an equation that is solved for and need to solve it for or vice versa. In the following example, we’re given an equation with both and on the same side and we’ll solve it for To do this, we will follow the same steps that we used to solve a formula for a specific variable.
Solve the formula for
when x = 4 | in general | |
Write the equation. | ||
Substitute any given values. | ||
Simplify if possible. | ||
Subtract to isolate the y -term. | ||
Simplify. | ||
Divide. | ||
Simplify. |
In the previous examples, we used the numbers in part (a) as a guide to solving in general in part (b). Do you think you’re ready to solve a formula in general without using numbers as a guide?
Solve the formula for
We will isolate
on one side of the equation.
We will isolate a on one side of the equation. | ||
Write the equation. | ||
Subtract b and c from both sides to isolate a . | ||
Simplify. |
So,
Solve the equation for
We will isolate
on one side of the equation.
We will isolate y on one side of the equation. | ||
Write the equation. | ||
Subtract 3 x from both sides to isolate y . | ||
Simplify. |
Solve the equation for
We will isolate
on one side of the equation.
We will isolate y on one side of the equation. | |
Write the equation. | |
Subtract to isolate the term with y . | |
Simplify. | |
Divide 5 to make the coefficient 1. | |
Simplify. |
Use the Distance, Rate, and Time Formula
In the following exercises, solve.
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