Lesson 8: Reasoning about Solving Equations (Part 2)

Reasoning about Solving Equations (Part 2)

Solve Another Equation

5 min

Problem

Solve the equation $3(x+4.5)=36$ . If you get stuck, use the diagram.

Balanced hanger diagram, left side, circle x, square 4 point 5, circle x, square 4 point 5, circle x, square 4 point 5, right side, rectangle 36.

Answer

7.5. Sample reasoning:

Divide each side by 3 leaving $x+4.5=12$ , then subtract 4.5 from each side.
The distributive property gives $3x+13.5=36$ . Subtract 13.5 from each side leaving $3x=22.5$ . Divide each side by 3.

Sample Response

7.5. Sample reasoning:

Divide each side by 3 leaving $x+4.5=12$ , then subtract 4.5 from each side.
The distributive property gives $3x+13.5=36$ . Subtract 13.5 from each side leaving $3x=22.5$ . Divide each side by 3.

Responding to Student Thinking

More Chancesmore_chances

Response: Students will have more opportunities to understand the mathematical ideas addressed here. There is no need to slow down or add additional work to the next lessons.

Standards

Addressing

7.EE.4.a·Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
7.EE.B.4.a·Solve word problems leading to equations of the form $px + q = r$ and $p(x + q) = r$, where $p$, $q$, and $r$ are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is $54$ cm. Its length is $6$ cm. What is its width?