(2−x)(5x+6)≥0

To solve the inequality (2−x)(5x+6)≥0, follow these steps:

Step 1: Set each factor equal to zero and solve for x.

2 - x = 0 5x + 6 = 0

Solving these gives x = 2 and x = -6/5.

Step 2: Plot these points on a number line.

Step 3: Test the intervals.

Choose a test point in each interval and substitute it into the inequality.

For x < -6/5, choose x = -2. Substituting x = -2 into the inequality gives (-4)(-4) which is positive. So, the inequality holds for x < -6/5.

For -6/5 < x < 2, choose x = 0. Substituting x = 0 into the inequality gives (2)(6) which is positive. So, the inequality holds for -6/5 < x < 2.

For x > 2, choose x = 3. Substituting x = 3 into the inequality gives (-1)(21) which is negative. So, the inequality does not hold for x > 2.

Step 4: Write the solution.

The solution to the inequality (2−x)(5x+6)≥0 is x ≤ 2 and x ≥ -6/5.