If you would like an in-depth review of fractions, click on Fractions.
Solve for x in the following equation.
Problem 5.5 c:
Simplify the equation by subtracting 1 from both sides of the equation..
Multiply both sides of the equation by an expression that represents the lowest common denominator. The expression is the smallest expression because it is the smallest expression that is divisible by all the denominators.
This expression is not easily factored. You can solve this equation using iteration or by graphing.
With iteration, choose two real numbers and evaluate
f(x)=2x3-21x2+55x-506 at each of the two numbers. You are looking for
a sign change. If there is a sign change, then you know that one real
solution is located between the two values you choose to test.
This indicates that a real solution exists between 0 and 20. Now narrow
the range to 10 and 20.
This indicates that real solution exists between 10 and 20. Narrow the
range again. Since -56 is close to 0, choose a number near 10.
You know a real solution exists between 10 and 11. Narrow the range
You know a real solution exists between 10 and 1.5. Narrow the range
You know a real solution exists between 10 and 10.25. Narrow the range
You know a real solution exists between 10.2 and 10.25. You can keep going until you have the accuracy you need in your answer.
You can also check your answer by graphing
If you would like to test yourself by working some problems similar to this example, click on problem.
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