solve the inequality [2x-7]>1 show your work
To solve the inequality [2x - 7] > 1, we need to isolate x by performing algebraic operations. Here's the step-by-step solution:
1. Start with the given inequality: [2x - 7] > 1.
2. Remove the absolute value brackets by considering two separate cases:
a. [2x - 7] > 1, if (2x - 7) > 1.
b. [2x - 7] > 1, if -(2x - 7) > 1.
3. Solve each case separately:
a. (2x - 7) > 1:
Add 7 to both sides of the inequality: 2x > 1 + 7.
Simplify: 2x > 8.
Divide both sides by 2 (since it is a positive number) to keep the inequality sign unchanged: x > 8/2.
Simplify: x > 4.
b. -(2x - 7) > 1
Multiply -1 to both sides of the inequality:
-2x + 7 > -1.
Subtract 7 from both sides: -2x > -1 - 7.
Simplify: -2x > -8.
Divide both sides by -2 (since it is a negative number, the inequality sign flips): x < -8/(-2).
Simplify: x < 4.
4. Combine the solutions from both cases:
x > 4 or x < 4.
Therefore, the inequality [2x - 7] > 1 is satisfied when x is greater than 4 or less than 4.