Graphing inequalities worksheet for math practice.
Worksheet titled "Inequalities" with ten problems involving graphing single variable inequalities on number lines.
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Step-by-step solution for: Single Variable Inequalities Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Single Variable Inequalities Worksheets
Here are the step-by-step solutions for each inequality. To graph these, we first solve for the variable (get it by itself) and then draw the solution on the number line.
1. $x \le 4 + 2$
* Solve: Add the numbers on the right side: $4 + 2 = 6$. So, $x \le 6$.
* Graph: Since the symbol is $\le$ (less than or equal to), put a solid dot at 6. Shade the arrow to the left because $x$ is smaller than 6.
2. $s > 12 + 3$
* Solve: Add the numbers: $12 + 3 = 15$. So, $s > 15$.
* Graph: Since the symbol is $>$ (greater than), put an open circle at 15. Shade the arrow to the right.
3. $9 < t$
* Solve: This reads "9 is less than t," which is the same as saying "$t$ is greater than 9" ($t > 9$).
* Graph: Put an open circle at 9. Shade the arrow to the right.
4. $84 + 6 \ge n$
* Solve: Add the numbers: $84 + 6 = 90$. So, $90 \ge n$, which means $n \le 90$.
* Graph: Put a solid dot at 90. Shade the arrow to the left.
5. $e < 3 + 20$
* Solve: Add the numbers: $3 + 20 = 23$. So, $e < 23$.
* Graph: Put an open circle at 23. Shade the arrow to the left.
6. $q \le 240 + 5$
* Solve: Add the numbers: $240 + 5 = 245$. So, $q \le 245$.
* Graph: The number line shows marks every 2 units (40, 42, 44...). 245 is halfway between 244 and 246. Put a solid dot at 245. Shade the arrow to the left.
7. $11 \times 11 \ge f$
* Solve: Multiply: $11 \times 11 = 121$. So, $121 \ge f$, which means $f \le 121$.
* Graph: The number line has marks every 2 units (115, 117...). 121 is halfway between 120 and 122. Put a solid dot at 121. Shade the arrow to the left.
8. $d > 217 + 7$
* Solve: Add the numbers: $217 + 7 = 224$. So, $d > 224$.
* Graph: The number line shows 30 and 40. Assuming standard spacing where each tick is 1 unit, 224 would be far off to the right. However, looking at the scale provided (ticks likely represent 1 unit based on previous problems), you would place an open circle at 224 and shade to the right. *Note: On the specific line provided for #8 which only shows 30 and 40, the answer 224 is off the chart, but mathematically the answer is $d > 224$.*
9. $u > 9 + 65$
* Solve: Add the numbers: $9 + 65 = 74$. So, $u > 74$.
* Graph: Put an open circle at 74. Shade the arrow to the right.
10. $2,046 + 33 \ge z$
* Solve: Add the numbers: $2,046 + 33 = 2,079$. So, $2,079 \ge z$, which means $z \le 2,079$.
* Graph: Put a solid dot at 2,079. Shade the arrow to the left.
Final Answer:
1. $x \le 6$ (Solid dot at 6, shade left)
2. $s > 15$ (Open circle at 15, shade right)
3. $t > 9$ (Open circle at 9, shade right)
4. $n \le 90$ (Solid dot at 90, shade left)
5. $e < 23$ (Open circle at 23, shade left)
6. $q \le 245$ (Solid dot at 245, shade left)
7. $f \le 121$ (Solid dot at 121, shade left)
8. $d > 224$ (Open circle at 224, shade right)
9. $u > 74$ (Open circle at 74, shade right)
10. $z \le 2,079$ (Solid dot at 2,079, shade left)
1. $x \le 4 + 2$
* Solve: Add the numbers on the right side: $4 + 2 = 6$. So, $x \le 6$.
* Graph: Since the symbol is $\le$ (less than or equal to), put a solid dot at 6. Shade the arrow to the left because $x$ is smaller than 6.
2. $s > 12 + 3$
* Solve: Add the numbers: $12 + 3 = 15$. So, $s > 15$.
* Graph: Since the symbol is $>$ (greater than), put an open circle at 15. Shade the arrow to the right.
3. $9 < t$
* Solve: This reads "9 is less than t," which is the same as saying "$t$ is greater than 9" ($t > 9$).
* Graph: Put an open circle at 9. Shade the arrow to the right.
4. $84 + 6 \ge n$
* Solve: Add the numbers: $84 + 6 = 90$. So, $90 \ge n$, which means $n \le 90$.
* Graph: Put a solid dot at 90. Shade the arrow to the left.
5. $e < 3 + 20$
* Solve: Add the numbers: $3 + 20 = 23$. So, $e < 23$.
* Graph: Put an open circle at 23. Shade the arrow to the left.
6. $q \le 240 + 5$
* Solve: Add the numbers: $240 + 5 = 245$. So, $q \le 245$.
* Graph: The number line shows marks every 2 units (40, 42, 44...). 245 is halfway between 244 and 246. Put a solid dot at 245. Shade the arrow to the left.
7. $11 \times 11 \ge f$
* Solve: Multiply: $11 \times 11 = 121$. So, $121 \ge f$, which means $f \le 121$.
* Graph: The number line has marks every 2 units (115, 117...). 121 is halfway between 120 and 122. Put a solid dot at 121. Shade the arrow to the left.
8. $d > 217 + 7$
* Solve: Add the numbers: $217 + 7 = 224$. So, $d > 224$.
* Graph: The number line shows 30 and 40. Assuming standard spacing where each tick is 1 unit, 224 would be far off to the right. However, looking at the scale provided (ticks likely represent 1 unit based on previous problems), you would place an open circle at 224 and shade to the right. *Note: On the specific line provided for #8 which only shows 30 and 40, the answer 224 is off the chart, but mathematically the answer is $d > 224$.*
9. $u > 9 + 65$
* Solve: Add the numbers: $9 + 65 = 74$. So, $u > 74$.
* Graph: Put an open circle at 74. Shade the arrow to the right.
10. $2,046 + 33 \ge z$
* Solve: Add the numbers: $2,046 + 33 = 2,079$. So, $2,079 \ge z$, which means $z \le 2,079$.
* Graph: Put a solid dot at 2,079. Shade the arrow to the left.
Final Answer:
1. $x \le 6$ (Solid dot at 6, shade left)
2. $s > 15$ (Open circle at 15, shade right)
3. $t > 9$ (Open circle at 9, shade right)
4. $n \le 90$ (Solid dot at 90, shade left)
5. $e < 23$ (Open circle at 23, shade left)
6. $q \le 245$ (Solid dot at 245, shade left)
7. $f \le 121$ (Solid dot at 121, shade left)
8. $d > 224$ (Open circle at 224, shade right)
9. $u > 74$ (Open circle at 74, shade right)
10. $z \le 2,079$ (Solid dot at 2,079, shade left)
Parent Tip: Review the logic above to help your child master the concept of introduction to inequalities worksheet.
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