Linear equations in one variable are introduced as a statement of equality when one of the numbers is unknown. The unknown number is represented by the variable. The linear equations consist of a sum or difference that equals a number.
To solve the equation, one must isolate the variable on one side of the equation. When the variable is isolated, the value on the other side of the equation is the value of the unknown number, and replacing the variable with that value makes a true statement. In earlier lessons, students have learned that you can add or subtract the same number to both sides of an equation without changing the equality. They use that knowledge in this lesson to isolate the variable and solve the equation.
The variable can be isolated in one step. If the expression with the unknown has a positive term, you subtract that value from both sides. If the expression with the unknown has a negative term, you add that value to both sides.
The resulting value is the value of the unknown and that value represents the solution to the equation.
In the problems in this lesson, the student must solve linear equations in one variable with a single expression equal to a given number and enter the solution.
In the prior lesson, students learn to solve linear equations in one variable when the solution requires a single operation of either addition or subtraction on each side of the equation.
In this lesson, they learn to solve similar equations in one variable when the solution requires a single operation of either multiplication or division on each side of the equation.
In this lesson, as in the prior one, students learn that to solve the equation, they must isolate the variable on one side of the equation.
The variable can be isolated in one step. If the expression with the unknown is a product, you divide each side by the known factor. If the expression with the unknown is a quotient, you multiply each side of the equation by the denominator.
The resulting value is the value of the unknown and that value represents the solution to the equation.
In the problems in this lesson, the student must solve linear equations in one variable with a single expression containing either a product or quotient that is equal to a given number and enter the solution.