Reading Inequality Symbols

Is the statement $8 > 5$ true or false?

Identify the symbol: The symbol $>$ means 'greater than' = Reading: '8 is greater than 5'

Check the relationship: Is 8 larger than 5? Yes! = 8 is indeed larger

Determine truth value: Since 8 IS greater than 5, the statement is TRUE = TRUE

Answer: True. The statement $8 > 5$ correctly shows that 8 is greater than 5.

Choosing the Correct Symbol

Fill in the blank: $-3 \,\square\, 2$

Visualize on number line: $-3$ is to the LEFT of $2$ on the number line = $-3$ is smaller

Recall the rule: Left on number line = smaller value = $-3 < 2$

Choose the symbol: Since $-3$ is less than $2$, use $<$ = $-3 < 2$

Answer: $-3 < 2$. Negative three is less than two.

Understanding 'Less Than or Equal To'

Is $4 \leq 4$ true?

Understand the symbol: $\leq$ means 'less than OR equal to' = Two conditions to check

Check 'less than': Is $4 < 4$? No, 4 is not less than itself = First condition: FALSE

Check 'equal to': Is $4 = 4$? Yes! = Second condition: TRUE

Apply OR logic: Since at least one condition is true, the whole statement is true = TRUE

Answer: True. While 4 is not less than 4, it IS equal to 4, so $4 \leq 4$ is true.

Real-World Inequality

A roller coaster requires riders to be at least 120 cm tall. Write this as an inequality using $h$ for height.

Identify the constraint: 'At least 120 cm' means 120 or more = Minimum height is 120

Choose the variable: Let $h$ = height of rider in cm = $h$ represents height

Write the inequality: Height must be 120 or greater: $h \geq 120$ = $h \geq 120$

Answer: $h \geq 120$. The rider's height must be greater than or equal to 120 cm.

Comparing Negative Numbers

Which is true: $-7 < -3$ or $-7 > -3$?

Place on number line: $-7$ is to the LEFT of $-3$ on the number line = $-7$ is further from zero

Apply the rule: Further left = smaller value = $-7$ is smaller

Choose correct inequality: Since $-7$ is less than $-3$, use $<$ = $-7 < -3$

Answer: $-7 < -3$. Remember: with negative numbers, the one further from zero is smaller!

Mistake: Confusing $<$ and $>$ symbols

Why: The symbols look similar and it's easy to mix them up.

Correct: The symbol 'points to' the smaller value. Think of it as an alligator mouth that always wants to eat the bigger number: $3 < 5$ (mouth opens toward 5).

Mistake: Thinking $-10 > -2$ because $10 > 2$

Why: With negative numbers, the larger digit doesn't mean a larger value.

Correct: Use the number line: $-10$ is further LEFT than $-2$, so $-10 < -2$. Think temperature: $-10°C$ is colder than $-2°C$.

Mistake: Confusing $\leq$ with 'less than'

Why: Students forget the 'or equal to' part.

Correct: $\leq$ means 'less than OR equal to'. So $5 \leq 5$ is TRUE because 5 equals 5.

Speed Limits and Traffic Rules

Traffic laws use inequalities to set maximum and minimum speeds.

A highway speed limit of 120 km/h means your speed $v$ must satisfy $v \leq 120$.

Shopping on a Budget

When shopping, you need to ensure your total stays within your budget.

If you have 50 euros, the total cost $c$ must satisfy $c \leq 50$.

Q: What's the difference between $<$ and $\leq$?

A: $<$ means strictly less than (not equal), while $\leq$ includes equality. So $3 < 3$ is false, but $3 \leq 3$ is true.

Q: How do I remember which symbol is which?

A: Think of the symbol as an alligator's mouth that always opens toward the bigger number. Or remember: the small end points to the small number.

Q: Can an inequality have no solutions?

A: Yes! For example, $x > 5$ AND $x < 3$ has no solution because no number is both greater than 5 and less than 3.