Equations and Inequalities

Lesson 1

Objective

Solve one-step equations with rational numbers.

Common Core Standards

Core Standards

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  • 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?

Foundational Standards

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  • 6.EE.B.5

  • 6.EE.B.7

Criteria for Success

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  1. Define and understand a solution to an equation as a number for a variable that makes the equation a true statement when substituted in.
  2. Solve one-step equations with rational numbers using addition, subtraction, multiplication, or division.
  3. Write and solve one-step equations for contextual situations. 

Tips for Teachers

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This lesson bridges a gap from 6.EE.7 to 7.EE.4a. Now that students have learned to compute with rational numbers, including those with negative values, those numbers are incorporated into one-step equations.

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Anchor Problems

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Problem 1

Is $${68}$$ a solution to $${{3\over4}x=51}$$? Why or why not? 

Guiding Questions

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Problem 2

What mistake did the student make in each example? What are the correct solutions? 

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References

Math Mistakes Photo: Solving Simple Equations

Solving Simple Equations by Michael Pershan is made available on Math Mistakes under the CC BY 3.0 license. © 2017 Math Mistakes, all rights reserved. Accessed Nov. 6, 2017, 9:18 a.m..

Problem 3

Find the value of $$x$$ in each equation below. Check your answer using substitution. 

a.  $$x - 14 = -5$$

b.   $$x + 8 = - 1$$

c.   $${1 \over 2}x=-14$$

d.   $$-{x \over 3}=-9$$

Guiding Questions

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Problem 4

A town's total allocation for firefighters’ wages and benefits in a new budget is $600,000. If wages are calculated at $40,000 per firefighter and benefits at $20,000 per firefighter, write an equation whose solution is the number of firefighters the town can employ if they spend their whole budget. Solve the equation.

Guiding Questions

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References

Illustrative Mathematics Firefighter Allocation

Firefighter Allocation, accessed on Nov. 6, 2017, 9:04 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set

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Target Task

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Problem 1

Solve each equation for $$x$$.

a.   $$x -24= -6$$

b.   $$-{{3}\over5}x=42$$

Problem 2

Trevor has $178 in his bank account at the start of the week. He makes one withdrawal during the week. At the end of the week, Trevor gets a notice from the bank that he has a negative balance of -$62. Write and solve an equation to determine how much money Trevor took out in his withdrawal.

Mastery Response

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