Mathematics 2008 JAMB Past Questions - Question 17: Find the range of values of x which satisfy the inequalities 4x-7 ≤ 3x and 3x-4 ≤ 4x.

Correct Answer

A

Explanation

4x - 7 < 3x4x - 3x < 7x < 7To find the range of values of x that satisfy the inequalities 4x - 7 ≤ 3x and 3x - 4 ≤ 4x, we can solve each inequality separately and then find the intersection of the solution sets.1. Solving the inequality 4x - 7 ≤ 3x:  Subtract 3x from both sides:  4x - 3x - 7 ≤ 0  x - 7 ≤ 0  Add 7 to both sides:  x ≤ 72. Solving the inequality 3x - 4 ≤ 4x:  Subtract 3x from both sides:  3x - 3x - 4 ≤ 0  -4 ≤ 0Now, let's consider the intersection of the solution sets:x ≤ 7 and -4 ≤ 0The range of values of x that satisfy both inequalities is the intersection of these two solution sets. Since -4 ≤ 0 is always true, it does not impose any restrictions on x. Therefore, the range of values of x that satisfy both inequalities is:x ≤ 7In other words, any value of x that is less than or equal to 7 will satisfy both inequalities.ii. 3x-4 < 4x3x - 4x < 4-x < 4x < -4-4 < x < 7To find the range of values of x that satisfy the given inequalities, let's solve them one by one.First, let's solve the inequality 4x - 7 ≤ 3x:4x - 7 ≤ 3xSubtract 3x from both sides:x - 7 ≤ 0Add 7 to both sides:x ≤ 7So, the solution to the first inequality is x ≤ 7.Now, let's solve the inequality 3x - 4 ≤ 4x:3x - 4 ≤ 4xSubtract 3x from both sides:-4 ≤ xSo, the solution to the second inequality is -4 ≤ x.Therefore, the range of values of x that satisfy both inequalities is -4 ≤ x ≤ 7.