What positive value for b makes the statement true? 6×b is less than 12 but greater than 6.
If you got this question from your homework, or a test, or something do not use the answer above. Actually try to figure it out yourself. The reason I am commenting is because my students took the exact same answer from here.
To find the positive value for b that makes the statement true, we need to solve the inequality 6×b < 12 and 6×b > 6.
Let's start with the first inequality:
6×b < 12
By dividing both sides of the inequality by 6, we get:
b < 2
Now, let's solve the second inequality:
6×b > 6
By dividing both sides of the inequality by 6, we get:
b > 1
So, the positive value for b that satisfies both inequalities is any value greater than 1 and less than 2.
To find the positive value for b that makes the statement true, we need to solve the inequality: 6×b < 12 and 6×b > 6.
Let's solve each part separately:
1. 6×b < 12: To isolate b, divide both sides of the inequality by 6: b < 12/6. Simplifying, we get b < 2.
2. 6×b > 6: Similarly, divide both sides of the inequality by 6: b > 6/6. Simplifying, we get b > 1.
Now, we have two inequalities: b < 2 and b > 1.
To find the common solution between these two inequalities, we look for a range of values that lies between 1 and 2.
Therefore, the positive value of b that satisfies both inequalities is any value greater than 1 but less than 2.
In interval notation, we can express the solution as: 1 < b < 2.
6 < 6 b < 12
so
1 < b < 2
well b = 1 1/2 works