solving the following rational equations and inequalities using the guided procedure on the table below
Answers
Answer:
If −3x+2−x−1x+2=52, then what is the largest real value of x?
Possible Answers:
−12
−1
2
1
12
Correct answer:
−12
Explanation:
We are asked to solve the equation −3x+2−x−1x+2=52.
Often, when solving equations involving rational expressions, it helps to elminate fractions by multiplying both sides of the equation by the denominators of each term intervolved.
In the context of this problem, we can first multiply both sides of the equation by x+2 to eliminate the denominator of the first term.
(x+2)(−3x+2−x−1x+2)=52(x+2)
Be sure to distribute the x+2 to each term on the left side of the equation.
−3(x+2)x+2−x(x+2)−x+2x+2(x+2)=52(x+2)
−3−x(x+2)−x+2x+2(x+2)=52(x+2)
Next, multiply both sides of the equation by x to elminate the term with an x in the denominator.
(x)(−3−x(x+2)−x+2x+2(x+2))=52(x+2)(x)
−3x−x(x)(x+2)−x(x+2)x+2(x+2)(x)=52(x+2)(x)
−3x−x(x)(x+2)−(x+2)+2(x+2)(x)=52(x+2)(x)
Then, multiply both sides of the equation by 2.
-12
Explanation:
To solve a reasonable inequality, we do the following steps:
Put the disparity in broad strokes.
Solve by setting the numerator and denominator to zero. The values you obtain are known as crucial values. A function's critical values are the points at which the function is either undefined or equal to 0. When the numerator is zero, the function is 0 as well. The function is undefined when the denominator is zero.
Plot the crucial values on a number line, dividing them into intervals.
Insert a test number from each interval into the original inequality. If it is true, then the interval from which it originated is included in the solution. If it makes a false assertion, the interval from which it originated will be terminated.