Question

where did the granite go on saturday night?
write the letter of each answer in the box containing the exercise number.
solve the inequality.

1. ( x + 12 < -4 ) 2. ( -3 geq x - 11 )
2. ( x - 6 < -7 ) 4. ( 2 geq x - 1 )
3. ( x + 9 < 10 ) 6. ( 12 + x > 8 )
4. ( x - (-14) geq 30 ) 8. ( x - 22 + 16 < -3 )
5. ( 5 > x - (-5) ) 10. ( 7 - 26 + x geq -11 )
6. ( 36 leq 6x - 5x - 16 )

write the sentence as an inequality. then solve the inequality.

1. a number ( x ) plus 24 is greater than 23.
2. a number ( x ) minus 5 is at least ( -4 ).
3. the sum of a number ( x ) and 19 is less than or equal to 35.
4. the number of minutes you can use on your prepaid cell phone is no more than 700 minutes. you have used 648 minutes. write and solve an inequality that represents how many more minutes you can use on your cell phone.
5. the side lengths of a triangle are 11.3 centimeters, 14.7 centimeters, and ( x ) centimeters. the perimeter of the triangle is less than 44 centimeters. write and solve an inequality to find the possible values of ( x ).

answers
f. ( x geq -16 )
l. ( x < 0 )
t. ( x < 3 )
y. ( x > -4 )
h. ( x geq 8 )
o. ( x leq 3 )
a. ( x leq 8 )
l. ( x < 1 )
a. ( x < -16 )
e. ( x < -1 )
t. ( x geq 52 )
l. ( x + 24 > 23; x > -1 )
c. ( x + 648 leq 700; x leq 52 )
s. ( x - 5 geq -4; x geq 1 )
r. ( x + 11.3 + 14.7 < 44; x < 18 )
b. ( x + 19 leq 35; x leq 16 )
grid with exercise numbers 11, 4, 7, 10, 3, 15, 16, 6, 13, 8, 1, 9, 14, 2, 5, 12

Explanation:

Problem 1: \( x + 12 < -4 \)

Step 1: Subtract 12 from both sides

To solve for \( x \), we subtract 12 from both sides of the inequality. This is based on the property of inequalities that allows us to add or subtract the same number from both sides without changing the direction of the inequality.
\( x + 12 - 12 < -4 - 12 \)

Step 2: Simplify both sides

Simplifying the left side gives \( x \), and simplifying the right side gives \( -16 \).
\( x < -16 \)

Step 1: Add 11 to both sides

We add 11 to both sides to isolate \( x \). Using the addition property of inequalities.
\( -3 + 11 \geq x - 11 + 11 \)

Step 2: Simplify both sides

Simplifying the left side: \( 8 \geq x \), which can be rewritten as \( x \leq 8 \)
\( x \leq 8 \)

Step 1: Add 6 to both sides

Add 6 to both sides to solve for \( x \), using the addition property of inequalities.
\( x - 6 + 6 < -7 + 6 \)

Step 2: Simplify both sides

Simplifying gives \( x < -1 \)
\( x < -1 \)

Answer:

\( x < -16 \) (corresponding to the answer with \( x < -16 \), likely the option with that solution)

Problem 2: \( -3 \geq x - 11 \)