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carroll.michael67 Jan 21, 2026 โ€ข 0 views

Solved examples: applying properties of inequality grade 7.

Hey there! ๐Ÿ‘‹ Inequalities got you scratching your head? Don't worry, I've got your back! Check out this quick guide and practice quiz. Let's ace this together! ๐Ÿ’ฏ
๐Ÿงฎ Mathematics

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๐Ÿ“š Quick Study Guide

    ๐Ÿ” Understanding Inequalities: Inequalities compare values that are not necessarily equal. We use symbols like < (less than), > (greater than), $\leq$ (less than or equal to), and $\geq$ (greater than or equal to).
    โž• Addition Property: Adding the same number to both sides of an inequality does not change the inequality. If $a < b$, then $a + c < b + c$.
    โž– Subtraction Property: Subtracting the same number from both sides of an inequality does not change the inequality. If $a > b$, then $a - c > b - c$.
    โœ–๏ธ Multiplication Property (Positive Number): Multiplying both sides of an inequality by a positive number does not change the inequality. If $a < b$ and $c > 0$, then $ac < bc$.
    โž— Division Property (Positive Number): Dividing both sides of an inequality by a positive number does not change the inequality. If $a > b$ and $c > 0$, then $\frac{a}{c} > \frac{b}{c}$.
    ๐Ÿ”„ Multiplication Property (Negative Number): Multiplying both sides of an inequality by a negative number reverses the inequality sign. If $a < b$ and $c < 0$, then $ac > bc$.
    โž— Division Property (Negative Number): Dividing both sides of an inequality by a negative number reverses the inequality sign. If $a > b$ and $c < 0$, then $\frac{a}{c} < \frac{b}{c}$.

Practice Quiz

  1. What is the solution to the inequality $x + 3 < 7$?
    1. $x < 4$
    2. $x > 4$
    3. $x < 10$
    4. $x > 10$
  2. Solve the inequality $y - 5 > 2$.
    1. $y > 7$
    2. $y < 7$
    3. $y > -3$
    4. $y < -3$
  3. What is the solution to $2z \leq 8$?
    1. $z \leq 4$
    2. $z \geq 4$
    3. $z \leq 16$
    4. $z \geq 16$
  4. Solve the inequality $\frac{w}{3} > 1$.
    1. $w > 3$
    2. $w < 3$
    3. $w > \frac{1}{3}$
    4. $w < \frac{1}{3}$
  5. If $-a > 5$, then which of the following is true?
    1. $a < -5$
    2. $a > -5$
    3. $a < 5$
    4. $a > 5$
  6. Solve $-3b \leq 9$.
    1. $b \geq -3$
    2. $b \leq -3$
    3. $b \geq 3$
    4. $b \leq 3$
  7. Which inequality is equivalent to $4c - 2 < 10$?
    1. $c < 3$
    2. $c > 3$
    3. $c < 2$
    4. $c > 2$
Click to see Answers
  1. A
  2. A
  3. A
  4. A
  5. B
  6. A
  7. A

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