Lesson 10: Different Options for Solving One Equation

Different Options for Solving One Equation

Solve Two Equations

5 min

Problem

Solve each equation. Explain or show your reasoning.

$8.88=4.44(x-7)$

$5\left(y+\frac25\right)=\text-13$

Answer

$x=9$ . Sample reasoning: After dividing both sides by 4.44, the equation is $2=x-7$ . After adding 7 to both sides, the equation is $x=9$ .
$y=\text-3$ . Sample reasoning: After distributing the 5, the equation is $5y+2=\text{-}13$ . After subtracting 2 from each side, it is $5y=\text{-}15$ . After dividing both sides by 5, it is $y=\text{-}3$ .

Sample Response

$x=9$ . Sample reasoning: After dividing both sides by 4.44, the equation is $2=x-7$ . After adding 7 to both sides, the equation is $x=9$ .
$y=\text-3$ . Sample reasoning: After distributing the 5, the equation is $5y+2=\text{-}13$ . After subtracting 2 from each side, it is $5y=\text{-}15$ . After dividing both sides by 5, it is $y=\text{-}3$ .

Responding to Student Thinking

Points to Emphasizepoints_to_emphasize

Response: If most students struggle with negative numbers when solving equations, plan to focus on strategies when opportunities arise over the next several lessons. For example, invite multiple students to share their thinking about how they solved the word problems in this activity:

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?