Solving Equations of the Form px+q=r Algebraically
Solving Equations of the Form px+q=r Algebraically is a Grade 7 math skill in Illustrative Mathematics, Chapter 6: Expressions, Equations, and Inequalities. Students apply inverse operations step by step to isolate the variable and find the solution, showing each algebraic manipulation explicitly.
Key Concepts
To solve an equation of the form $px + q = r$, use inverse operations to isolate the variable. First, undo the addition or subtraction of the constant term $q$. Then, undo the multiplication by the coefficient $p$.
Common Questions
How do you solve px+q=r algebraically?
Apply inverse operations step by step. First subtract q from both sides (px equals r minus q), then divide both sides by p (x equals (r minus q) divided by p).
What does solving algebraically mean?
Solving algebraically means showing each step of manipulating the equation, applying the same operation to both sides to maintain balance, until x is isolated.
What is an example of solving px+q=r algebraically?
Solve 5x minus 3 equals 17. Add 3 to both sides: 5x equals 20. Divide both sides by 5: x equals 4.
How is the algebraic method different from other methods?
The algebraic method uses formal notation to show every step explicitly, unlike estimation or inspection, making it clear and systematic for all types of linear equations.
What chapter covers algebraic equation solving in Illustrative Mathematics Grade 7?
Solving equations px+q=r algebraically is covered in Chapter 6: Expressions, Equations, and Inequalities in Illustrative Mathematics Grade 7.