Reasoning about Solving Equations (Part 1)

Solve the Equation

5 min

Problem

Solve the equation. If you get stuck, use the diagram.

5x+14=614\displaystyle 5x+\frac14=\frac{61}{4}

Balanced hanger. Left side, 5 circles labeled x, square labeled 1 fourth. Right side, rectangle labeled 61 fourths.

Answer

x=3x=3

Sample Response

x=3x=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. <em>For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?</em>
  • 7.EE.B.4.a·Solve word problems leading to equations of the form <span class="math">\(px + q = r\)</span> and <span class="math">\(p(x + q) = r\)</span>, where <span class="math">\(p\)</span>, <span class="math">\(q\)</span>, and <span class="math">\(r\)</span> 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. <span>For example, the perimeter of a rectangle is <span class="math">\(54\)</span> cm. Its length is <span class="math">\(6\)</span> cm. What is its width?</span>