Solving Equations of the Form px+q=r
Solving Equations of the Form px+q=r is a Grade 7 math skill in Illustrative Mathematics, Chapter 6: Expressions, Equations, and Inequalities. Students solve two-step equations by first subtracting or adding q from both sides, then dividing or multiplying by p.
Key Concepts
To solve a two step equation of the form $px+q=r$, we use inverse operations to isolate the variable. The goal is to find the value of $x$ that makes the equation true.
The general procedure is: 1. Undo the addition or subtraction of the constant term ($q$). 2. Undo the multiplication or division by the coefficient ($p$).
Common Questions
How do you solve equations of the form px+q=r?
First, subtract q from both sides to isolate the px term: px equals r minus q. Then divide both sides by p to find x equals (r minus q) divided by p.
What is an example of solving px+q=r?
Solve 3x plus 4 equals 19. Subtract 4: 3x equals 15. Divide by 3: x equals 5.
What order do you perform the steps?
Undo addition or subtraction first (subtract q), then undo multiplication or division last (divide by p). This reverses the order of operations in which the equation was built.
How do you check a solution to px+q=r?
Substitute your solution back into the original equation. If both sides are equal, your answer is correct.
What chapter covers solving px+q=r in Illustrative Mathematics Grade 7?
Solving equations of the form px+q=r is covered in Chapter 6: Expressions, Equations, and Inequalities in Illustrative Mathematics Grade 7.