Inequality
Symbols
Symbols
This symbol means “greater than.”
>
Is (2,3) a solution to x+y>4? Explain
Yes. 2+3=5, and 5>4
Should the boundary line for y>2x+1 be dashed or solid?
Dashed line
Games cost $2 and rides cost $3. You can spend no more than $30
2x+3y≤30
A student graphs y>2x+1 using a solid line. What is the mistake?
The boundary line should be dashed because >> does not include points on the line
This symbol means “less than or equal to.”
≤
Is (4,1) a solution to 2x+y≤10?
Yes, 2(4)+1=9, and 9≤10
Should the boundary line for y≤−x+4 be dashed or solid?
Solid line
Adult tickets cost $8, and student tickets cost $5. You must collect at least $100.
8x+5y≥100
A student graphs y≤−x+4 using a dashed line. What is the mistake?
The boundary line should be solid because < includes points on the line.
This symbol represents “at least.”
What is ≥
Is (3,2) a solution to 2x+3y<12?
2(3)+3(2)=12, and 12 is not less than 12
For y<3x−2, do you shade above or below the dashed line?
Shade below
Notebooks cost $3, and folders cost $2. You have less than $24 to spend.
3x+2y<24
A student substitutes (2,3) into 2x+y≤8 and writes 2(3)+2≤8. What is the mistake?
The student switched the x- and y-values. It should be 2(2)+3≤8.
This symbol represents “no more than.”
What is ≤
Is (−1,4) a solution to y≥2x+5?
Yes, 4≥2(−1)+5, or 4≥3
For y≥−2x+3, do you shade above or below the line?
Shade above
A truck carries 20-pound boxes and 30-pound crates. It can carry at most 600 pounds.
20x+30y≤600
A student graphs y>−2x+5 and shades below the line. What is the mistake?
The student should shade above the line because y is greater than −2x+5.
Explain the difference between < and ≤
< excludes the number; ≤ includes it
Is (5,3) a solution to 4x+2y≥28?
No, 4(5)+2(3)=26, and 26 is not ≥28
Describe how to graph 2x+y>6, including the boundary line and shading.
Graph y>−2x+6. Use a dashed line and shade above it.
A school needs at least 50 volunteers. Adults and students can volunteer.
x+y≥50
A student writes 4x+3y≥244x+3y\ge24 for “Spend no more than $24.” What is the mistake?
No more than” means less than or equal to. The inequality should be 4x + 3y ≤ 24.