find the whole number solutions to each of these inequalities.
q1. 3<2x-1≤17
q2. 5≤g-3≤12
q3. 8<5c≤20
q2.
add three to all sides:
8<= g<=15
the others are very similar.
To find the whole number solutions to each of these inequalities, we need to solve them step by step. Here's how you can approach each question:
q1. 3 < 2x - 1 ≤ 17
1. Add 1 to all parts of the inequality to isolate the variable: 3 + 1 < 2x - 1 + 1 ≤ 17 + 1
This simplifies to: 4 < 2x ≤ 18
2. Divide all parts of the inequality by 2 to solve for x: 4/2 < 2x/2 ≤ 18/2
This simplifies to: 2 < x ≤ 9
The whole number solutions to the inequality are x = 3,4,5,6,7,8,9.
q2. 5 ≤ g - 3 ≤ 12
1. Add 3 to all parts of the inequality to isolate the variable: 5 + 3 ≤ g - 3 + 3 ≤ 12 + 3
This simplifies to: 8 ≤ g ≤ 15
The whole number solutions to the inequality are g = 8,9,10,11,12,13,14,15.
q3. 8 < 5c ≤ 20
1. Divide all parts of the inequality by 5 to solve for c: 8/5 < 5c/5 ≤ 20/5
This simplifies to: 1.6 < c ≤ 4
Since we are looking for whole number solutions, we can round up 1.6 to 2 and round down 4 to 4. Therefore, the whole number solutions to the inequality are c = 2,3,4.
Remember, in these inequalities, the "less than" (<) and "less than or equal to" (≤) signs indicate that the variable can be any value less than or equal to the given number, while the "greater than" (>) and "greater than or equal to" (≥) signs indicate that the variable can be any value greater than or equal to the given number.