7th Grade Math · Unit 4
Solve the inequality, then show its solutions on a number line.
Open or closed
Use an open circle for < and >. Use a closed circle for ≤ and ≥.
A closed circle includes that number. An open circle does not.
Which way to shade
Shade right for greater. Shade left for less.
Use the symbol you have after the inequality is solved.
Test a number
A number is a solution only when it makes the solved inequality true.
That includes the boundary when the circle is closed.
Solve a short inequality, then draw the ray.
2x > 8
Divide both sides by 2.
x > 4
Use a open circle at 4 and shade to the right.
Answer: x > 4
3x < 9
Divide both sides by 3.
x < 3
Use a open circle at 3 and shade to the left.
Answer: x < 3
x + 4 ≥ 7
x + 4 − 4 ≥ 7 − 4
x ≥ 3
Use a closed circle at 3 and shade to the right.
Answer: x ≥ 3
2x ≤ 6
Divide both sides by 2.
x ≤ 3
Use a closed circle at 3 and shade to the left.
Answer: x ≤ 3
4x > 16
Divide both sides by 4.
x > 4
Use a open circle at 4 and shade to the right.
Answer: x > 4
x + 5 < 8
x + 5 − 5 < 8 − 5
x < 3
Use a open circle at 3 and shade to the left.
Answer: x < 3
5x ≥ 10
Divide both sides by 5.
x ≥ 2
Use a closed circle at 2 and shade to the right.
Answer: x ≥ 2
x + 2 ≤ 6
x + 2 − 2 ≤ 6 − 2
x ≤ 4
Use a closed circle at 4 and shade to the left.
Answer: x ≤ 4
3x + 1 > 10
3x + 1 − 1 > 10 − 1
3x > 9
Divide both sides by 3.
x > 3
Use a open circle at 3 and shade to the right.
Answer: x > 3
2x + 4 < 12
2x + 4 − 4 < 12 − 4
2x < 8
Divide both sides by 2.
x < 4
Use a open circle at 4 and shade to the left.
Answer: x < 4
6x ≥ 12
Divide both sides by 6.
x ≥ 2
Use a closed circle at 2 and shade to the right.
Answer: x ≥ 2
Solve a two-step inequality, then draw the ray.
2x + 3 > 11
2x + 3 − 3 > 11 − 3
2x > 8
Divide both sides by 2.
x > 4
Use a open circle at 4 and shade to the right.
Answer: x > 4
3x + 2 < 14
3x + 2 − 2 < 14 − 2
3x < 12
Divide both sides by 3.
x < 4
Use a open circle at 4 and shade to the left.
Answer: x < 4
2x + 5 ≥ 13
2x + 5 − 5 ≥ 13 − 5
2x ≥ 8
Divide both sides by 2.
x ≥ 4
Use a closed circle at 4 and shade to the right.
Answer: x ≥ 4
4x + 1 ≤ 17
4x + 1 − 1 ≤ 17 − 1
4x ≤ 16
Divide both sides by 4.
x ≤ 4
Use a closed circle at 4 and shade to the left.
Answer: x ≤ 4
5x + 3 > 18
5x + 3 − 3 > 18 − 3
5x > 15
Divide both sides by 5.
x > 3
Use a open circle at 3 and shade to the right.
Answer: x > 3
2x + 1 < 9
2x + 1 − 1 < 9 − 1
2x < 8
Divide both sides by 2.
x < 4
Use a open circle at 4 and shade to the left.
Answer: x < 4
3x + 6 ≥ 21
3x + 6 − 6 ≥ 21 − 6
3x ≥ 15
Divide both sides by 3.
x ≥ 5
Use a closed circle at 5 and shade to the right.
Answer: x ≥ 5
4x + 3 ≤ 19
4x + 3 − 3 ≤ 19 − 3
4x ≤ 16
Divide both sides by 4.
x ≤ 4
Use a closed circle at 4 and shade to the left.
Answer: x ≤ 4
6x + 2 > 20
6x + 2 − 2 > 20 − 2
6x > 18
Divide both sides by 6.
x > 3
Use a open circle at 3 and shade to the right.
Answer: x > 3
2x + 7 < 17
2x + 7 − 7 < 17 − 7
2x < 10
Divide both sides by 2.
x < 5
Use a open circle at 5 and shade to the left.
Answer: x < 5
3x + 4 ≥ 16
3x + 4 − 4 ≥ 16 − 4
3x ≥ 12
Divide both sides by 3.
x ≥ 4
Use a closed circle at 4 and shade to the right.
Answer: x ≥ 4
Solve first. Then test four numbers.
2x ≤ 6
Divide both sides by 2.
x ≤ 3
Test each number in the solved inequality.
1 is a solution
3 is a solution
4 is not a solution
6 is not a solution
Answer: 1, 3
2x + 1 < 7
2x + 1 − 1 < 7 − 1
2x < 6
Divide both sides by 2.
x < 3
Test each number in the solved inequality.
1 is a solution
2 is a solution
3 is not a solution
5 is not a solution
Answer: 1, 2
3x > 12
Divide both sides by 3.
x > 4
Test each number in the solved inequality.
2 is not a solution
4 is not a solution
5 is a solution
6 is a solution
Answer: 5, 6
x + 4 ≤ 9
x + 4 − 4 ≤ 9 − 4
x ≤ 5
Test each number in the solved inequality.
3 is a solution
5 is a solution
6 is not a solution
8 is not a solution
Answer: 3, 5
2x + 3 ≥ 11
2x + 3 − 3 ≥ 11 − 3
2x ≥ 8
Divide both sides by 2.
x ≥ 4
Test each number in the solved inequality.
2 is not a solution
4 is a solution
5 is a solution
7 is a solution
Answer: 4, 5, 7
4x < 8
Divide both sides by 4.
x < 2
Test each number in the solved inequality.
0 is a solution
1 is a solution
2 is not a solution
3 is not a solution
Answer: 0, 1
5x + 1 > 16
5x + 1 − 1 > 16 − 1
5x > 15
Divide both sides by 5.
x > 3
Test each number in the solved inequality.
1 is not a solution
3 is not a solution
4 is a solution
6 is a solution
Answer: 4, 6
−2x > 8
Divide both sides by −2. The inequality symbol reverses.
x < −4
Test each number in the solved inequality.
−6 is a solution
−5 is a solution
−4 is not a solution
−2 is not a solution
Answer: −6, −5
−3x + 6 < 0
−3x + 6 − 6 < 0 − 6
−3x < −6
Divide both sides by −3. The inequality symbol reverses.
x > 2
Test each number in the solved inequality.
1 is not a solution
2 is not a solution
3 is a solution
5 is a solution
Answer: 3, 5
−4x + 8 ≤ 0
−4x + 8 − 8 ≤ 0 − 8
−4x ≤ −8
Divide both sides by −4. The inequality symbol reverses.
x ≥ 2
Test each number in the solved inequality.
0 is not a solution
2 is a solution
3 is a solution
5 is a solution
Answer: 2, 3, 5
−12x + 5 > 1
−12x + 5 − 5 > 1 − 5
−12x > −4
Divide both sides by −12. The inequality symbol reverses.
x < 8
Test each number in the solved inequality.
4 is a solution
6 is a solution
8 is not a solution
10 is not a solution
Answer: 4, 6
Need help with this skill?
Book a Session with Amy