Solve each inequality algebraically:how do I solve this problem? What is the answer? Show the work.
x+4/x-2 less than equal 1 thanks for your help
(x+4)/(x-2) <= 1
If x-2>0, then
x+4 <= x-2
4 < -2
no solutions there
If x-2 < 0,
x+4 >= x-2
4 >= -2
so all x's are a solution. But our condition was that x-2 < 0, so
x < 2
Makes sense, since there is a horizontal asymptote at y = 1 and a vertical asymptote at x = 2
6 is less than equal 0
To solve the inequality algebraically, follow these steps:
Step 1: Set up the inequality.
The given inequality is x + 4 / (x - 2) ≤ 1.
Step 2: Determine the restriction.
In this case, the fraction (x - 2) cannot equal 0 because dividing by zero is undefined. Therefore, we have x ≠ 2.
Step 3: Get rid of the fraction.
To eliminate the fraction, multiply both sides of the inequality by (x - 2). Doing this preserves the inequality direction.
(x - 2) * (x + 4) / (x - 2) ≤ (x - 2) * 1
Simplifying, we get:
(x + 4) ≤ (x - 2)
Step 4: Solve the linear inequality.
Expand the brackets:
x + 4 ≤ x - 2
Step 5: Collect like terms and isolate the variable.
Subtracting x from both sides:
4 ≤ -2
Step 6: Evaluate the inequality.
Since 4 is not less than or equal to -2, the original equation is not true for any possible values of x.
Therefore, the answer is no solution.