Find the solution set for the following inequality: x+1>1/2x-11
x+1 > x/2 - 11
subtract x/2 + 1 from each side:
x/2 > -12
multiply by 2
x > -24
To find the solution set for the inequality x + 1 > 1/2x - 11, follow these steps:
Step 1: Simplify both sides of the inequality.
Starting with x + 1 > 1/2x - 11, begin by subtracting 1/2x from both sides:
x + 1 - (1/2x) > 1/2x - 11 - (1/2x)
Simplifying this gives:
x + 1 - 1/2x > - 11
Combining like terms:
(2x/2) + (1 - 1/2)x > - 11
x/2 + 1/2x > - 11
Step 2: Combine similar terms.
In this case, we can multiply everything by 2 to get rid of the denominator:
2(x/2) + 2(1/2x) > - 11 * 2
x + 1 > - 22
Step 3: Isolate the variable.
Subtract 1 from both sides of the inequality:
x + 1 - 1 > - 22 - 1
x > - 23
Therefore, the solution set for the inequality x + 1 > 1/2x - 11 is x > -23.