Solve and graph equation & inequalities for 6th grade: Worksheets, Tips & Tricks

In 6^th grade math, inequalities are mathematical statements that compare two expressions using symbols like <, >, ≤, or ≥. For example, 3 < 5 means 3 is less than 5, and 7 ≥ 7 means 7 is greater than or equal to 7.

We can also use a variable, such as x, to represent an unknown number in an inequality. For example, x + 2 > 10 means that whatever number x is, if you add 2 to it, you get a number greater than 10.

To solve an inequality, we need to find all the possible values of the variable that make the inequality true. For example, to solve x + 2 > 10, we’ll subtract 2 from both sides of the inequality and get x > 8. This means that any number greater than 8 will make the inequality true.

To graph an inequality on a number line, we need to mark the boundary point (the number that separates the solutions from the non-solutions) with an open circle if the inequality does not include the equal sign (< or >), or with a closed circle if it does (≤ or ≥). Then, we’ll shade the number line part containing the solutions. For example;

To graph x > 8, we need to mark 8 with an open circle and shade the part of the number line to the right of 8.

Apart from worksheets, tips, and tricks, we will provide some fun activities to enhance 6^th graders solving inequalities with variables skills.

One way to practice inequalities with variables is to use cards with numbers and symbols. Students can shuffle the cards and deal four cards to each player. Then, each player has to use their cards to make an inequality statement.

For example, if you have cards with 2, x, <, and 9 on them, you can make the statement 2x < 9. The player with the highest value of x wins the round.

 

Another way to practice inequalities with variables is to use dice and a spinner with symbols on it. You can roll two dice and use them as the numbers in your inequality statement. Then, you can spin the spinner and use the symbol that lands on as the comparison symbol in your statement.

For example, if you roll a 4 and a 6, and the spinner lands on >, you can make the statement 4 > 6. The player with the accurate statement wins the round.

There are many reasons why inequalities are important for real-world problems. One such is modeling real-world situations that involve comparisons or limitations. For example, if you want to buy a shirt that costs $15 and have $20 in your pocket, you can write an inequality to represent how much money you will have left after buying the shirt: 20 - 15 ≥ x. This means you will have at least $5 left after buying the shirt.

We can also use inequalities to represent constraints or conditions that must be met. For example, if you want to join a club requiring a grade point average (GPA) of at least 3.5 out of 4.0, you can write an inequality to represent this requirement: GPA ≥ 3.5. This means your GPA must be greater than or equal to 3.5 to join the club.

Are your 6th-grade students ready for some challenge? They can try these 10 inequality questions from Mathskills4kids.com and see how well they understand equations and inequalities.

1) Which inequality is equivalent to -3x + 5 ≤ -13?

1. x ≥ -6
2. x ≤ -6
3. x ≥ -8
4. x ≤ -8

2) Which graph represents the solution set of x + 4 > -2?

1. A number line with a closed circle at -6 and shading to the left of it.
2. A number line with an open circle at -6 and shading to the left of it.
3. A number line with a closed circle at -2 and shading to the right of it.
4. A number line with an open circle at -2 and shading to the right of it.

3) Which value of x makes the inequality -2x + 7 < -5 true?

1. x = -6
2. x = 6
3. x = -3
4. x = 3

4) Which inequality is represented by the graph below?

1. x < -4
2. x ≤ -4
3. x > -4
4. x ≥ -4

5) Which inequality describes the situation? You must score at least 80 points on your final exam to pass the course.

1. x + 80 ≥ 100
2. x - 80 ≥ 100
3. 80 + x ≥ 100
4. 80 - x ≥ 100

6) Which situation can be modeled by the inequality 3x + 2 ≤ 11?

1. You have $11 and want to buy candy bars for $3 each and gum packs for $2 each. How many candy bars and gum packs can you buy?
2. You have $11 and want to buy books that cost $3 each and magazines that cost $2 each. How many books and magazines can you buy?
3. You have $11 and want to save $3 and spend $2 each week. How many weeks will it take you to save all your money?
4. You have $11 and want to earn $3 and spend $2 each week. How many weeks will it take you to spend all your money?

7) Which value of x is a solution of the inequality 2x - 5 > x + 1?

1. x = -6
2. x = -4
3. x = 4
4. x = 6

8) Which graph represents the solution set of the compound inequality -2 ≤ x < 5?

1. A number line with a closed circle at -2, an open circle at 5, and shading between them.
2. A number line with an open circle at -2, a closed circle at 5, and shading between them.
3. A number line with a closed circle at -2, an open circle at 5, and shading outside them.
4. A number line with an open circle at -2, a closed circle at 5, and shading outside them.

9) Which situation can be modeled by the inequality x/4 + 3 > 5?

1. You have $3 and want to buy cupcakes that cost $4 each. How many cupcakes can you buy and still have over $5 left?
2. You have $3 and want to sell cupcakes that cost $4 each. How many cupcakes do you need to sell to make more than $5 profit?
3. You have 3 hours and want to watch movies lasting 4 hours each. How many movies can you watch and still have over 5 hours left?
4. You have 3 hours and want to make movies that last 4 hours each. How many movies do you need to make to use more than 5 hours?

10) Which value of x is not a solution of the inequality |x - 2| < 3?

1. x = -1
2. x = 0
3. x = 1
4. x = 5