One-Step Inequalities
Solve: x + 4 < -88
x < -92
Solve: 2x -1 < 9
x < 5
When graphing inequalities, which symbols have an open circle?
less than < and greater than >
A number is greater than 1.
x > 1
A delivery driver took 5.2 hours to complete a route. He wants to complete it in fewer than 4.5 hours next time. By how many hours must he need to reduce his time? Write an inequality to represent the situation.
5.2 - x < 4.5
Solve: 3z ≥ 15.
z ≥ 5
Solve: -3(3n + 3) < 6n
n > -1
Which direction do we shade for x < -3?
left of -3
One fourth of a number is at most 7.
1/4 x ≤ 7
A movie theater ticket costs $6. You have at most $30 to spend. Write an inequality to represent the number of tickets you can buy.
6x ≤ 30
Solve: z/20 > 20
z > 400
Solve: 3a + 9 > 5 (a - 3)
a < 12
Graph the solution set for -x > -5.
Graph should have an open circle on -5 and values left of -5 shaded :)
Two times a number plus seven is less than or equal to 7.
2x + 7 ≤ 7
Lena is saving money. She already has $15 and saves $5 per week. Write an inequality to represent the number of weeks w she must save to have at least $60.
15 + 5w ≥ 60
Solve: - x/3 ≥ -6
x ≤ 18
Solve: -5(2-b) ≥ 3(b+4)
b ≤ 11
Graph the solution set for 2/3 x ≤ 8.
Graph should have a closed circle on 12 and values to the left of 12 should be shaded.
The difference of five times a number and three is greater than negative 2.
5x - 3 > -2
A music club needs at least 40 total members. There are already 18 members. New members can join in groups of 4 per week. Write an inequality to determine the minimum number of weeks w needed.
18 + 4w ≥ 40
Solve 10j ≤ 9j - 8
j ≤ -8
Solve: - 2(y + 5) + 22 > 2(6 - y)
no solution!
What inequality is represented by a graph where values to the left of -2 are shaded and there is a closed circle on -2?
x ≤ -2
The difference of three times a number and six is at least the sum of fifteen and twenty times a number.
3x - 6 ≥ 15 + 20x
Pedro, Sebastian, and Manuel are each one year apart in age. The sum of their ages is greater than the age of their father, who is 60. Write an inequality to represent this situation, where x is the age of the youngest brother.
x + (x+1) + (x+2) > 60 *answer: x>19