6.EE.B.8 6th Grade Expressions & Equations

Inequalities & Their Graphs

Write an inequality of the form x > c or x < c to represent a constraint, and represent its solutions on a number line diagram.

How to explain it

At this standard, students write inequalities (x > c, x < c) from real-world constraints (6.EE.B.8), graph solutions on number lines with open circle and shading, and check whether specific values are solutions via substitution (6.EE.B.5-IQ carry-forward from #25). Ramp: P1-4 solution-check, P5-8 write from words, P9-14 graph with number-line visual, P15-16 integrated.

The anchor students hold onto: x > c: shade right · x < c: shade left

This closes the 6th Grade EE strand. Inequality forms extend to 7th grade EE. Next: Statistics and Probability -- #27 Measures of Center (6.SP.B.5a+5b) -- mean, median, and data distributions.

Worked examples

Example 1 Writing an Inequality

Fewer than 6 students absent.

Step 1'Fewer than' means less than -- use <

Step 2'6 students' -> c = 6; unknown -> variable n

Step 3Inequality: n < 6

Answern < 6

Example 2 Checking a Solution

Is n = 2 a solution to n > 1?

Step 1Substitute n = 2: is 2 > 1?

Step 22 > 1 -- TRUE

Step 3YES -- n = 2 IS a solution

AnswerYES -- n = 2 is a solution

Common mistakes

What students write Shading in the wrong direction -- shading left for x > c or right for x < c.

The fix > means GREATER THAN -- shade right toward larger values. < means LESS THAN -- shade left.

Try this Student work: "a plant must grow taller than 48 cm" h < 48 (WRONG) A student wrote h < 48 for "a plant must grow taller than 48 centimeters." Find and fix the error. Then check if h = 50 is a solution to your corrected inequality.

What students write Drawing a filled circle at the boundary instead of an open circle for strict > and <.

The fix x > c and x < c do NOT include the boundary value -- always use an OPEN circle.

Teacher tip

Head off the two predictable errors before they happen. First: > means GREATER THAN -- shade right toward larger values. < means LESS THAN -- shade left. Second: x > c and x < c do NOT include the boundary value -- always use an OPEN circle.