Write & Graph Inequalities · MCAP 6.EE.B.8

Learning Goal: Write inequalities of the form x > c or x < c for real-world constraints and graph them on a number line.

Vocabulary

inequalityA statement comparing values with >, <, ≥, or ≤.

greater than (>)Larger than; x > 4 means x is any number bigger than 4.

less than (<)Smaller than; x < 4 means x is any number smaller than 4.

open circleA hollow dot on a number line showing the endpoint is NOT included (used for > or <).

at least / at most'At least' means ≥ (that value or more); 'at most' means ≤ (that value or less).

What You Need to Know

x > c and x < c have infinitely many solutions, not just one number.
Graph with an OPEN circle on c for > or < because c itself is not included.
For x > c, shade to the RIGHT (larger numbers); for x < c, shade to the LEFT (smaller numbers).
'More than' means >, 'less than' means <, 'fewer than' means <.
'At least' means ≥ and 'at most' means ≤, which use a CLOSED (filled) circle.
Read the arrow direction from the variable: x > 5 points the shading toward bigger numbers.

Worked Example I Do — watch how it works

A ride requires riders to be more than 48 inches tall. Write and graph an inequality for the allowed height h.

Step 1. 'More than 48' means h is greater than 48: h > 48.
Step 2. Place an open circle at 48 because exactly 48 is not allowed.
Step 3. Shade the line to the right of 48 to show all heights greater than 48.

Answer: h > 48; open circle at 48, shaded right

Guided Practice We Do — try it together

1. Write an inequality for 'a number x is less than 10' and describe its graph.
💡 Hint: 'Less than' uses < and shades toward smaller numbers.
2. A savings goal needs more than $25. Write an inequality for amount m.
💡 Hint: 'More than' means greater than.
3. Graph x > 3: filled or open circle, and which way do you shade?
💡 Hint: > uses an open circle; shade toward larger numbers.

Independent Practice You Do — show your work

1. Write an inequality for 'x is greater than 7.'
2. Write an inequality for 'a number n is fewer than 12.'
3. For x < 5, is the circle open or closed?
4. A speed limit allows speeds at most 35 mph. Write an inequality for speed s.
5. For x > 0, which direction do you shade?

MCAP-Style Practice

Directions: Answer each item the way you would on the MCAP. For selected-response items, fill in the circle (○) next to the correct answer. For constructed-response items, enter your answer and show your work. Every item below assesses standard 6.EE.B.8.

Item 1Selected Response6.EE.B.8

Which inequality means 'a number x is greater than 6'?

Select the correct answer.

○ A. x < 6○ B. x > 6○ C. x = 6○ D. x ≤ 6

Item 2Selected Response6.EE.B.8

The graph of x < 4 has which features?

Select the correct answer.

○ A. Closed circle at 4, shaded right○ B. Open circle at 4, shaded right○ C. Open circle at 4, shaded left○ D. Closed circle at 4, shaded left

Item 3Constructed Response6.EE.B.8

To enter a contest, players must be younger than 13. Write an inequality for the age a.

Enter your answer in the space provided. Show your work.

Enter your answer:

Teacher Answer Key (click to show)

Independent 1	x > 7
Independent 2	n < 12
Independent 3	Open
Independent 4	s ≤ 35
Independent 5	Right (toward larger numbers)
Item 1 · 6.EE.B.8	B — 'Greater than 6' is written x > 6, with an open circle at 6.
Item 2 · 6.EE.B.8	C — x < 4 uses an open circle (4 not included) and shades left toward smaller numbers.
Item 3 · 6.EE.B.8	a < 13 — 'Younger than 13' means a is less than 13, with an open circle at 13 and shading left.

Neft Teacher · Grade 6 MCAP Mathematics Review · Standard 6.EE.B.8