Grade 8 Math Inequalities

Introduction to grade 8 math inequalities:
In mathematics, an inequalities is a statement about the relative size or order of two objects or about whether they are the same or not.

The notation a < b means that a is less than b.
The notation a > b means that a is greater than b.
The notation a ? b means that a is not equal to b.
In this article we shall discuss about math grade 8 inequalities. (Source: Wikipedia)

Grade 8 math inequalities example problem


Here we are going to discuss some 8th grade inequalities problems with detailed solutions.

Example:

Solving the inequalities 5x – 12 > 4x +12

Solution:

The given inequalities is

5x – 12 > 4x +12

Adding the 12 on both side of equation

5x -12+12> 4x +12+12

5x>4x+24

Subtract 4x on both side of the inequality equation

x>24

Example:

Solving the following inequality equation -5< 4(x+2)-5<19 br="">
Solution:

The given inequality is

-5< 4(x+2)-5<19 br="">
Multiplying the factor for given inequality equation

-5<4x br="">
-5<4x br="">
Subtracting three on both sides of the inequality equation

-5-3<4x br="">
-8<4x br="">
Divide by 4 for all terms in inequality

-2
Conclusion:

The solution includes all real number value the interval is (-2, 4)

Example:

Solving the following inequality equation -4< 2(x+6)-2<12 br="">
Solution:

Given inequality is

-4< 2(x+6)-2<12 br="">
Multiplying factor values for given inequality equation

-4<2x br="">
-4<2x br="">
Subtracting 10 on both sides of equation

-4-10<2x br="">
-14<2x br="">
Divide by 2 for all terms in equation

-7
Conclusion:

The solution includes all real number value the interval is (-7, 1)

Example:

Solving the inequality 6x – 4 > 3x +14

Solution:

The given inequality is

6x – 4 > 3x +14

Adding the value four on both side of equation

6x -4+4> 3x +14+4

6x>3x+18

Subtract value 3x on both side of the equation

3x>18

Simplifying the value x

x>18/3

x>6

Conclusion:

The solution includes all real number value the interval is (6, infinity)

Example:

Solving the inequality 8x – 2 > 3x +13

Solution:

The given inequality is

8x – 2 > 3x +13

Adding the value two on both side of equation

8x -2+2> 3x +13+2

8x>3x+15

Subtract value 3x on both side of the equation

5x>15

Simplifying the value x

x>15/5

x>3

Conclusion:

The solution includes all real number value the interval is (3, infinity)

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Grade 8 math inequalities practice problem


Problem:

Solving the inequality -4< 4(x+2)-4<16 br="">
Answer:

The solution includes the interval is (-2, 3)

Problem:

Solving the inequality equation -2< 4(x+6)-3<10 br="">
Answer:

The solution includes all real number value the interval is (-6, -2.75)