Answer:
To find the number of integral solutions for x in the given inequality, we can first solve the inequality to find the range of values that x can take on. To do this, we need to isolate the x term on one side of the inequality, so let's start by subtracting 9 from both sides of the inequality:
-69 ≤ 7x + 9 ≤ 49
-9 ≤ 7x ≤ 40
Next, we can divide both sides of the inequality by 7 to isolate the x term:
-9/7 ≤ x ≤ 40/7
The result of this calculation is a range of values for x, but we are looking for the number of integral solutions, which means we need to find the number of whole numbers that x can take on within this range. In this case, we can see that the range of possible values for x is from -1 to 5, and there are 5 whole numbers within this range (-1, 0, 1, 2, 3, 4, 5), so there are 5 integral solutions for x in this inequality.
In general, to find the number of integral solutions for x in an inequality of the form a ≤ bx + c ≤ d, where a, b, c, and d are constants, you can follow these steps:
1.Solve the inequality to isolate the x term on one side, by subtracting c from both sides and then dividing both sides by b. This will give you the range of possible values for x.
2.Count the number of whole numbers within this range to find the number of integral solutions for x.
Explanation: