Question

consider the inequality 7 + 4x > x - 2. select all the values of x that are solutions. a. x = -3 b. x = 0 c. x = 3 d. x = -6 e. x = 6

Explanation:

Step1: Solve the inequality \(7 + 4x > x - 2\)

Subtract \(x\) from both sides: \(7 + 4x - x > -2\)
Simplify: \(7 + 3x > -2\)
Subtract 7 from both sides: \(3x > -2 - 7\)
Simplify: \(3x > -9\)
Divide both sides by 3: \(x > -3\)

Step2: Check each option

• Option A: \(x = -3\). Since \(x > -3\) (not including -3), \(x = -3\) is not a solution.
• Option B: \(x = 0\). Since \(0 > -3\), \(x = 0\) is a solution.
• Option C: \(x = 3\). Since \(3 > -3\), \(x = 3\) is a solution.
• Option D: \(x = -6\). Since \(-6 < -3\), \(x = -6\) is not a solution.
• Option E: \(x = 6\). Since \(6 > -3\), \(x = 6\) is a solution.

Answer:

B. \(x = 0\), C. \(x = 3\), E. \(x = 6\)