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Not Equal: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Not EqualNot Equal: Definition and ExampleTable of ContentsDefinition of Not Equal Symbol in Mathematics

The not equal sign (≠) is a mathematical symbol used to represent two quantities that are not equal in value. It appears as two horizontal parallel lines cut by a slanted line, essentially an equal sign with a slash through it. This symbol allows mathematicians to concisely express inequality between values without writing lengthy statements. The not equal sign is part of a family of comparison symbols in mathematics that includes less than (), greater than (>>>), less than or equal to (≤\leq≤), and greater than or equal to (≥\geq≥).

When we write A≠BA ≠ BA=B, we're stating that quantity A does not have the same value as quantity B. This inequality can apply to various attributes such as numerical values, sizes, or measurements. For example, we might express that the price of a tomato is not equal to the price of an apple, or that the size of a tennis ball is not equal to the size of a basketball. The symbol provides a clear and efficient way to express these relationships in mathematical notation.

Examples of Not Equal Symbol in Problems Example 1: Solving an Equation and Determining Inequality Problem:

Solve the following equation: 6b−35=556b - 35 = 556b−35=55 and find whether b=12b = 12b=12 or not.

Step-by-step solution:

First, let's organize the equation so we can isolate the variable bbb: 6b−35=556b - 35 = 556b−35=55

Next, add 35 to both sides of the equation to move all constant terms to the right side: 6b−35+35=55+356b - 35 + 35 = 55 + 356b−35+35=55+35 6b=906b = 906b=90

Then, divide both sides by 6 to find the value of bbb: 6b6=906\frac{6b}{6} = \frac{90}{6}66b​=690​ b=15b = 15b=15

Finally, compare this result with the given value 12: Since 15≠1215 ≠1215=12, we can conclude that b≠12b ≠ 12b=12.

Example 2: Comparing Percentage Spent Problem:

Bella spent $18 out of her $20 pocket money. John spent $13 out of $15. Calculate whether the percentage of money spent by each one of them is equal or not.

Step-by-step solution:

First, calculate the percentage of money spent by Bella: Percentage spent by Bella=1820×100\text{Percentage spent by Bella} = \frac{18}{20} \times 100Percentage spent by Bella=2018​×100

Next, simplify the fraction by dividing both numerator and denominator by 2: 1820=910\frac{18}{20} = \frac{9}{10}2018​=109​

Then, multiply by 100 to get the percentage: 910×100=90%\frac{9}{10} \times 100 = 90\%109​×100=90%

Now, calculate the percentage of money spent by John: Percentage spent by John=1315×100\text{Percentage spent by John} = \frac{13}{15} \times 100Percentage spent by John=1513​×100

Next, this fraction can be rewritten as: 1315=133×15=133×25%\frac{13}{15} = \frac{13}{3} \times \frac{1}{5} = \frac{13}{3} \times 25\%1513​=313​×51​=313​×25% =86.66%= 86.66\%=86.66%

Finally, compare the two percentages: Since 90%≠86.66%90\% ≠ 86.66\%90%=86.66%, the percentage of money spent by Bella is not equal to the percentage of money spent by John.

Example 3: Comparing Weight of Chocolate Packets Problem:

Packet A contains 8 chocolates, and each chocolate weighs 4 ounces. Packet B has 12 chocolates, and each chocolate weighs 2 ounces. Find whether the two packets are equal in terms of weight.

Step-by-step solution:

First, determine the total weight of chocolates in Packet A: Total weight of Packet A=Number of chocolates×Weight per chocolate\text{Total weight of Packet A} = \text{Number of chocolates} \times \text{Weight per chocolate}Total weight of Packet A=Number of chocolates×Weight per chocolate =8×4 ounces= 8 \times 4 \text{ ounces}=8×4 ounces =32 ounces= 32 \text{ ounces}=32 ounces

Next, calculate the total weight of chocolates in Packet B: Total weight of Packet B=Number of chocolates×Weight per chocolate\text{Total weight of Packet B} = \text{Number of chocolates} \times \text{Weight per chocolate}Total weight of Packet B=Number of chocolates×Weight per chocolate =12×2 ounces= 12 \times 2 \text{ ounces}=12×2 ounces =24 ounces= 24 \text{ ounces}=24 ounces

Then, compare the total weights of both packets: Packet A weighs 32 ounces and Packet B weighs 24 ounces.

Finally, since 32 ounces≠24 ounces32 \text{ ounces} ≠ 24 \text{ ounces}32 ounces=24 ounces, we can conclude that the two packets are not equal in terms of weight.

Comments(6)EEngineerChrisNovember 5, 2025I've used this not equal definition with my students. It's super clear, and the examples really help them grasp the concept in different scenarios!

NNatureLover85September 17, 2025I’ve been using the not equal examples from this page to help my kids with math homework, and it’s made a big difference! The real-world comparisons were super helpful for explaining it clearly.

NNatureLover89September 10, 2025I used this page to explain the 'not equal' symbol to my daughter, and it really clicked for her! The examples made it so much easier to connect with real-life situations. Thanks for making math less intimidating!

NNatureLover45August 27, 2025I’ve used the 'Not Equal' examples on this page to help my kid understand comparisons in math. The practical examples made it so much easier for them to grasp the concept!

NNatureLover75August 20, 2025I’ve been using this page to help my kids understand the not equal sign, and it’s been a game-changer! The examples made it so easy to explain real-life comparisons. Thanks for making math less stressful!

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