Solving rational equation becomes easy once you understand the problem. A rational equation is a type of equation where it involves at least one rational expression,
Solving Equation Containing Rational Solutions:
We saw how to solve a two-step algebraic equation:
8x – 7 = 0
the variable appears on the left side of the equation; however, there is the constant -7 that we must eliminate to isolate the variable x. So the first step is to do the opposite and add 7 to each side of the equation:
8x – 7 + 7 = 0 + 7 or
8x = 7
8𝑥/8 = 7/8
Simplifying we have,
x = 7/8
let’s do one more sample problem and solve
2 = -11x + 7
2 – 7 = -11x + 7 – 7
-5 = -11x
since the variable is multiplied -11, we do the inverse operation and divide each side of the equation by -11
−5/−𝟏𝟏 = −11𝑥/−𝟏𝟏
Melissa has a total of $14, which is exactly four times more than the money that Tanya has, plus another $9. How much money does Tanya have?
step 1: Extract the key information that is given:
- Melissa has $14.
- Melissa has 4 times more than what Tanya has plus $9.
step 2: What are we trying to find:
- The amount that Tanya has.
step 3: Assign variables to any quantities that are unknown
Let t = the amount of money (in dollars) that Tanya has
let’s write an equation with the unknown t and solve for t:
4t + 9 = 14
Solving this equation, we find t = 1¼ = 1.25.
So in answer to the original question, we have determined that Tanya has $1.25 (notice we have used a dollar sign which shows the proper units of the answer). Typically an answer to a word problem will have two parts, the numeric (or number) answer along with the proper units. Sometimes problems are missed because the numeric portion is correct, but the units are wrong. Had we written 1.25¢, this answer would have been incorrect since the units are dollars and not cents. We know the units are dollars since we added 9 to 4t in the initial equation—and the 9 represented $9. We also used 14 in the initial equation which again represented $14. Had we used 900 instead of 9, to represent 900¢ and set the expression equal to 1400¢, we would have solved for t which represented the unknown number of cents that Tanya had. Using units of cents in our equation, we obtain
t = 125, and 125¢ = $1.25, which is equivalent to the same answer that we previously obtained using units of dollars
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