Question

activity 1
describe each of the inequalities in words.
model the inequality ( x>5 ) means _.
answer ( x ) is greater than 5

1. the inequality ( y<6 ) means _.
2. the inequality ( 5 leq x ) means _.
3. the inequality ( z>9 ) means _.
4. the inequality ( m geq 10 ) means _.
5. the inequality ( 17>n ) means _.

activity 2
tell whether each of the statements is true or false.
model if ( x>20 ), a possible value of ( x ) is 19.
answer: false

1. if ( y leq 22 ), a possible value of ( y ) is 22.
2. if ( 60>z ), a possible value of ( z ) is 59.
3. if ( w geq 34 ), a possible value of ( w ) is 46.
4. if ( x<22 ), a possible value of ( x ) is 22.

activity 3
draw each inequality on a number line.

1. ( m leq 15 )
2. ( n geq 0 )
3. ( x<35 )
4. ( y>-5 )

Explanation:

Activity 1

• For \(y < 6\), the symbol \( < \) means "less than".
• For \(5\leq x\), the symbol \(\leq\) means "less than or equal to".
• For \(z > 9\), the symbol \(>\) means "greater than".
• For \(m\geq 10\), the symbol \(\geq\) means "greater than or equal to".
• For \(17 > n\), the symbol \(>\) means "greater than".

• For \(y\leq 22\), the symbol \(\leq\) includes the value \(22\).
• For \(60 > z\), \(59\) is less than \(60\).
• For \(w\geq 34\), \(46\) is greater than \(34\).
• For \(x < 22\), \(22\) is not less than \(22\).

• For \(m\leq 15\): Draw a closed circle at \(15\) (because of \(\leq\)) and shade to the left.
• For \(n\geq 0\): Draw a closed circle at \(0\) (because of \(\geq\)) and shade to the right.
• For \(x < 35\): Draw an open circle at \(35\) (because of \( < \)) and shade to the left.
• For \(y > - 5\): Draw an open circle at \(-5\) (because of \(>\)) and shade to the right.

Answer:

1. \(y\) is less than \(6\)
2. \(5\) is less than or equal to \(x\)
3. \(z\) is greater than \(9\)
4. \(m\) is greater than or equal to \(10\)
5. \(17\) is greater than \(n\)

Activity 2