 # Find Solutions to Make Equations True

Videos and solutions to help Grade 6 students learn the definition of solution in the context of placing a value into a variable to see if it makes the equation true.

New York State Common Core Math Module 4, Grade 6, Lesson 24

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Common Core For Grade 6

Lesson 25 Student Outcomes

• Students learn the definition of solution in the context of placing a value into a variable to see if it makes the equation true.

Lesson 25 Summary

Variable: A variable is a symbol (such as a letter) that represents a number (i.e., it is a placeholder for a number).
A variable is a placeholder for "a" number that does not "vary".
Expression: An expression is a numerical expression, or a result of replacing some (or all) of the numbers in a numerical expression with variables.
Equation: An equation is a statement of equality between two expressions.
If A and B are two expressions in the variable x, then A = B is an equation in the variable x.

Opening Exercise

Identify a value for the variable that would make each equation or inequality into a true number sentence. Is this the only possible answer? State when the equation or inequality is true using equality and inequality symbols.
1. 3 + g = 15
2. 30 > 2d
3. 15/f > 5
4. 42 ≤ 50 - m

Example 1
Each of the following numbers, if substituted for the variable, makes one of the equations below into a true number sentence. Match the number to that equation: 3, 6, 15, 16, 44.
a. n + 26 = 32
b. n - 12 = 32
c. 17n = 51
d. 42 = n
e. n/3 = 15

Problem Set
Find the solution to each equation.
1. 43 = y
2. 8a = 24
3. 32 = g - 4
4. 56 = j + 29
5. 48/r = 12
6. k = 15 - 9
7. x·1/5 = 60
8. m + 3.45 = 12.8
9. a = 15

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