Introduction
Two algebraic expressions or two real numbers related by the symbol '<', '>', '<=' or '>=' form an linear inequality.
Examples of numerical inequalities: 3 < 5; 7 > 5 x < 5;
Examples of literal inequalities: y > 2; x <= 3, y >= 4.
3 > x > 5 (read as x is greater than or equal to 3 and less than 5) and 2 < y < 4 are the examples of double inequalities.
How to solve linear inequality:
Added or subtracted by the same number on both side of the inequality.
Multiplied or divided by the same number on both side of the inequality but if we divide or multiply by a negative number, we must reverse the inequality sign.
Worked Examples for Linear Inequalities :
Example 1:
Solve the linear inequality: 5x – 3 < 7
Solution:
5x – 3 < 7
Add 3 on both side of the equation
5x - 3 + 3 < 7 + 3
5x < 10
Divide by 5 on both side of the equation
5x / 5 < 10 / 5
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Example 2:
Solve the linear inequality: 7x + 3 < 5x + 9
Solution:
7x + 3 < 5x + 9
Subtract 3 to the both side of the equation
7x + 3 - 3 < 5x + 9 -3
7x < 5x + 6
Subtract 5x on both sides of the equation
7x - 5x < 5x + 6 - 5x
2x<6 2="" both="" br="" by="" divide="" equation="" of="" on="" sides="" the="">
2x / 2 < 6 / 2
x < 3
So, the solution is (-infinity, 3).
I am planning to write more post on show me how to multiply fractions, how to solve and graph linear inequalities. Keep checking my blog.
Additional Linear Inequality Examples
Example 3: Solve the linear inequality: 5x – 3 < 3x +1
Solution:
5x – 3 < 3x +1
Add 3 to the both side of the equation
5x – 3+3 < 3x +1+3
5x < 3x + 4
Subtract 3x on both sides of the equation
5x - 3x < 4
2x < 4
Divide by 2 on both side of the equation
2x / 2 < 4 / 2
x<2 2="" br="" inequality="" infinity="" is="" range="" so="" the="">
Example 4: Solve the linear inequality: 37 – (3x + 5) > 9x – 8 (x – 3)
Solution:
37 – (3x + 5) > 9x – 8 (x – 3)
37- 3x - 5 > 9x - 8x + 24
-3x + 32 > 1x + 24
Subtract x on both sides of the equation
-3x+32- x > 1x + 24 - x
-4x +32 > 24
Subtract 32 on both sides of the equation
-4x + 32-32 > 24 - 32
-4x > -8
Divide by -4 on both sides of the equation and change the inequality sign
-4x / -4 < -8 / -4
x < 2 So, the solution is (-infinity, 2)
Two algebraic expressions or two real numbers related by the symbol '<', '>', '<=' or '>=' form an linear inequality.
Examples of numerical inequalities: 3 < 5; 7 > 5 x < 5;
Examples of literal inequalities: y > 2; x <= 3, y >= 4.
3 > x > 5 (read as x is greater than or equal to 3 and less than 5) and 2 < y < 4 are the examples of double inequalities.
How to solve linear inequality:
Added or subtracted by the same number on both side of the inequality.
Multiplied or divided by the same number on both side of the inequality but if we divide or multiply by a negative number, we must reverse the inequality sign.
Worked Examples for Linear Inequalities :
Example 1:
Solve the linear inequality: 5x – 3 < 7
Solution:
5x – 3 < 7
Add 3 on both side of the equation
5x - 3 + 3 < 7 + 3
5x < 10
Divide by 5 on both side of the equation
5x / 5 < 10 / 5
x<2 2="" br="" infinity="" is="" so="" solution="" the="">
Example 2:
Solve the linear inequality: 7x + 3 < 5x + 9
Solution:
7x + 3 < 5x + 9
Subtract 3 to the both side of the equation
7x + 3 - 3 < 5x + 9 -3
7x < 5x + 6
Subtract 5x on both sides of the equation
7x - 5x < 5x + 6 - 5x
2x<6 2="" both="" br="" by="" divide="" equation="" of="" on="" sides="" the="">
2x / 2 < 6 / 2
x < 3
So, the solution is (-infinity, 3).
I am planning to write more post on show me how to multiply fractions, how to solve and graph linear inequalities. Keep checking my blog.
Additional Linear Inequality Examples
Example 3: Solve the linear inequality: 5x – 3 < 3x +1
Solution:
5x – 3 < 3x +1
Add 3 to the both side of the equation
5x – 3+3 < 3x +1+3
5x < 3x + 4
Subtract 3x on both sides of the equation
5x - 3x < 4
2x < 4
Divide by 2 on both side of the equation
2x / 2 < 4 / 2
x<2 2="" br="" inequality="" infinity="" is="" range="" so="" the="">
Example 4: Solve the linear inequality: 37 – (3x + 5) > 9x – 8 (x – 3)
Solution:
37 – (3x + 5) > 9x – 8 (x – 3)
37- 3x - 5 > 9x - 8x + 24
-3x + 32 > 1x + 24
Subtract x on both sides of the equation
-3x+32- x > 1x + 24 - x
-4x +32 > 24
Subtract 32 on both sides of the equation
-4x + 32-32 > 24 - 32
-4x > -8
Divide by -4 on both sides of the equation and change the inequality sign
-4x / -4 < -8 / -4
x < 2 So, the solution is (-infinity, 2)
