solev the compound inequality 2x-9/8<-7 or 2x-9/8>6
2x-9/8<-7
2x<-7+9/8=-47/8
x<-47/16
2x-9/8>6
2x > (48+9)/8 = 57/8
x > 57/16
Therefore
x<-47/16 or x > 57/16
To solve the compound inequality 2x - 9/8 < -7 or 2x - 9/8 > 6, we will solve each inequality separately and find the intersection of the solutions.
Let's start with the first inequality: 2x - 9/8 < -7
Step 1: Add 9/8 to both sides of the inequality to isolate the variable.
2x - 9/8 + 9/8 < -7 + 9/8
2x < -7 + 9/8
Step 2: Simplify the right side of the inequality.
2x < -7 + 9/8
2x < -56/8 + 9/8
2x < -47/8
Step 3: Divide both sides of the inequality by 2 to solve for x.
2x/2 < -47/8 / 2
x < -47/16
So, the solution to the first inequality is x < -47/16.
Now, let's solve the second inequality: 2x - 9/8 > 6
Step 1: Add 9/8 to both sides of the inequality to isolate the variable.
2x - 9/8 + 9/8 > 6 + 9/8
2x > 6 + 9/8
Step 2: Simplify the right side of the inequality.
2x > 6 + 9/8
2x > 48/8 + 9/8
2x > 57/8
Step 3: Divide both sides of the inequality by 2 to solve for x.
2x/2 > 57/8 / 2
x > 57/16
So, the solution to the second inequality is x > 57/16.
To find the intersection of the solutions, we need to find the values of x that satisfy both inequalities. In other words, we need to find the values of x that are less than -47/16 and greater than 57/16. However, there is no intersection between these two solutions since there are no values of x that can be simultaneously less than -47/16 and greater than 57/16.
Therefore, the compound inequality 2x - 9/8 < -7 or 2x - 9/8 > 6 has no solution.