Let’s use equations to represent stories and see what it means to solve equations.
The following diagram shows what is a true and false equation, variable, solution and coefficient.
The equation a + b = c could be true or false.
a. If a is 3, b is 4, and c is 5, is the equation true or false?
b. Find new values of a, b, and c that make the equation true.
c. Find new values of a, b, and c that make the equation false.
2. The equation x · y = z could be true or false.
a. If x is 3, y is 4, and z is 12, is the equation true or false?
b. Find new values of x, y, and z that make the equation true.
c. Find new values of x, y, and z that make the equation false.
Scroll down the page for the solutions to the “Are you ready for more?” section.
Here are three situations and six equations. Which equation best represents each situation? If you get stuck, draw a diagram.
Here are some equations that contain a variable and a list of values. Think about what each equation means and find a solution in the list of values. If you get stuck, draw a diagram. Be prepared to explain why your solution is correct.
One solution to the equation a + b + c = 10 is a = 2, b = 5, c = 3.
How many different whole-number solutions are there to the equation a + b + c = 10? Explain or show your reasoning.
A coefficient is a number that is multiplied by a variable.
For example, in the expression 3x + 5, the coefficient of x is 3. In the expression y + 5, the coefficient of y is 1, because y = 1 · y.
solution to an equation
A solution to an equation is a number that can be used in place of the variable to make the equation true.
For example, 7 is the solution to the equation m + 1 = 8, because it is true that 7 + 1 = 8. The solution to m + 1 = 8 is not 9, because 9 + 1 ≠ 8.
A variable is a letter that represents a number. You can choose different numbers for the value of the variable.
For example, in the expression 10 - x, the variable is x. If the value of x is 3, then 10 - x = 7, because 10 - 3 = 7. If the value of x is 6, then 10 - x = 4, because 10 - 6 = 4.
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