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Understand Solving an Equation or Inequality as a Process of Answering a Question

For each problem, substitute the given value and decide: does it make the equation or inequality true or false?

Grade 6·19 problems·~25 min·Common Core Math - Grade 6·standard·6-ee-b-5
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

If n=6n = 6, what is the value of n+4n + 4?

2.

If you substitute n=4n = 4 into 2n2n, what is the result?

3.

Which statement about the inequality symbol > is correct?

B

Fluency Practice

1.

Test candidates from the set {5,10,13,15}\{5, 10, 13, 15\} for the equation n−4=9n - 4 = 9. Which value is the solution?

2.

Which value from the set {4,6,8,12}\{4, 6, 8, 12\} makes 3y=183y = 18 true?

3.

Does m=7m = 7 make the equation 2m+1=152m + 1 = 15 true?

4.

From the set {2,4,6,8,10}\{2, 4, 6, 8, 10\}, which values make 2x<122x < 12 true?

5.

For the inequality x<5x < 5, is x=5x = 5 a solution?

C

Varied Practice

1.

Substitute each candidate into x+3=8x + 3 = 8 and decide whether the equation is true or false.

x=2x = 2: Write TRUE or FALSE:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

x=5x = 5: Write TRUE or FALSE:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

The solution is x=x =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

result for x=2:
result for x=5:
solution:
2.

Test each value in {7,8,9,11}\{7, 8, 9, 11\} for the inequality t+2>9t + 2 > 9. Which value is on the boundary and does NOT satisfy the strict inequality?

3.

For the equation 4a=204a = 20, which statement correctly describes the solution?

Table for testing several x-values in the inequality 3x greater than 9, with the true-or-false results left blank.
4.

For the inequality 3x>93x > 9, Mia tests x=4x = 4 and finds it true. She says, "The solution is x=4x = 4." What is wrong with her statement?

5.

The inequality n>4n > 4 is satisfied by which of the following?

D

Word Problems / Application

1.

A bag of apples costs pp dollars. Kezia buys one bag and pays with a 10 dollar bill. Her change is 3 dollars. The equation is p+3=10p + 3 = 10. Which value of pp from {5,7,9}\{5, 7, 9\} makes this equation true?

2.

A classroom rule says: "Fewer than 30 students may be in this room." Let ss represent the number of students. The inequality is s<30s < 30.

How many of the following values satisfy the inequality? Values to test: 28, 30, 31, 15.

E

Error Analysis

1.

Diego looked at x+3=8x + 3 = 8 and said: "The solution is xx because xx is the variable in the equation."

What error did Diego make?

2.

Toni tested x=3x = 3 for the inequality 2x<122x < 12: 2(3)=6<122(3) = 6 < 12. True! She wrote: "The solution is x=3x = 3."

What error did Toni make?

F

Challenge

1.

An equation has one solution, but an inequality has many solutions. Explain in your own words why this is true, using an example equation and an example inequality.

2.

The equation x2=9x^2 = 9 has solutions from the set {−3,0,3,6}\{-3, 0, 3, 6\}. Which values in this set are solutions?

0 of 19 answered