SOLVING INEQUALITIES WITH VARIABLES ON BOTH SIDES WORKSHEET
About "Solving inequalities with variables on both sides worksheet"
Solving inequalities with variables on both sides worksheet :
Here we are going to see some practice questions on solving inequalities with variables on both sides.
Solving inequalities with variables on both sides worksheet - Practice questions
(1) Solve the following linear inequality
3x - 7 > x + 1
(2) Solve the following linear inequality
x + 5 > 4x - 10
(3) Solve the following linear inequality
3x + 9 ≥ -x + 19
(4) Solve the following linear inequality
3x + 17 ≤ 2(1 - x)
Solving inequalities with variables on both sides worksheet - Solution
Question 1 :
Solve the following linear inequality
3x - 7 > x + 1
Solution :
3x - 7 > x + 1
Subtract x on both sides
3x - x - 7 > x - x + 1
2x - 7 > 1
Add 7 on both sides
2x - 7 + 7 > 1 + 7
2x > 8
Divide by 2 on both sides
2x/2 > 8/2
x > 4
Hence the solution set of the given inequality is (4, ∞)
Question 2 :
Solve the following linear inequality
x + 5 > 4x - 10
Solution :
x + 5 > 4x - 10
Subtract 4x on both sides
x - 4x + 5 > 4x - 4x - 10
-3x + 5 > -10
Subtract 5 on both sides
-3x + 5 - 5 > -10 - 5
-3x > -15
Divide by -3 on both sides
x < 5
Hence the solution set of the given inequality is (-∞, 5)
Question 3 :
Solve the following linear inequality
3x + 9 ≥ -x + 19
Solution :
3x + 9 ≥ -x + 19
Add x on both sides
3x + x + 9 ≥ -x + x + 19
4x + 9 ≥ 19
Subtract 9 on both sudes
4x + 9 - 9 ≥ 19 - 9
4x ≥ 10
Divide by 4 on both sides
x ≥ 10/4
x ≥ 5/2
Hence the solution set of the given inequality is [5/2, ∞)
Since we have grater than or equal sign, we have used closed parentheses to write 5/2.
Question 4 :
Solve the following linear inequality
3x + 17 ≤ 2(1 - x)
Solution :
3x + 17 ≤ 2(1 - x)
By using distributive property on the right side, we get
3x + 17 ≤ 2 - 2x
Add 2x on both sides
3x + 2x + 17 ≤ 2 - 2x + 2x
5x + 17 ≤ 2
Subtract 17 on both sides
5x + 17 - 17 ≤ 2 - 17
5x ≤ -15
Divide by 5 on both sides
x ≤ -15/5
x ≤ -3
Hence the solution set of the given inequality is (-∞, -3]
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