Two Methods for Solving p(x+q)=r
Two Methods for Solving p(x+q)=r is a Grade 7 math skill in Illustrative Mathematics, Chapter 6: Expressions, Equations, and Inequalities. Students learn to solve this equation form either by distributing p first then solving, or by dividing by p first to isolate (x+q) then subtracting q.
Key Concepts
An equation of the form $p(x+q)=r$ can be solved using two different, equally valid methods: 1. Divide First: Divide both sides by $p$ to get $x+q = \frac{r}{p}$. 2. Distribute First: Apply the distributive property to get $px+pq = r$.
Common Questions
What are the two methods for solving p(x+q)=r?
Method 1: Distribute p to get px plus pq equals r, then solve as a two-step equation. Method 2: Divide both sides by p first to get x plus q equals r/p, then subtract q.
Which method is easier: distributing or dividing first?
If p divides evenly into r, dividing first is simpler. If r/p is not a whole number, distributing first may be easier. Choose based on the numbers.
What is an example using Method 1 (distribute)?
Solve 3(x plus 4) equals 21. Distribute: 3x plus 12 equals 21. Subtract 12: 3x equals 9. Divide by 3: x equals 3.
What is an example using Method 2 (divide first)?
Solve 3(x plus 4) equals 21. Divide by 3: x plus 4 equals 7. Subtract 4: x equals 3.
What chapter covers p(x+q)=r in Illustrative Mathematics Grade 7?
Two methods for solving p(x+q)=r are covered in Chapter 6: Expressions, Equations, and Inequalities in Illustrative Mathematics Grade 7.