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.
(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)
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]
After having gone through the stuff given above, we hope that the students would have understood "Solving inequalities with variables on both sides worksheet".
Apart from the stuff given above, if you want to know more about "Solving inequalities with variables on both sides worksheet", please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits