Learn on PengiBig Ideas Math, Course 2Chapter 3: Expressions and Equations

Lesson 5: Solving Two-Step Equations

In this Grade 7 lesson from Big Ideas Math, Course 2, students learn to solve two-step equations by applying the Addition, Subtraction, Multiplication, and Division Properties of Equality in sequence. Using algebra tiles and algebraic steps, they work through equations involving integers and fractions, such as isolating the variable by first adding or subtracting a constant and then dividing or multiplying. The lesson also connects two-step equations to real-life problem-solving strategies like working backwards, meeting Florida Standard MAFS.7.EE.2.4a.

Section 1

Equations with Two Operations

Property

To solve an equation with two or more operations, we must isolate the variable on one side of the equation. We undo the operations in reverse order. Typically, we undo addition or subtraction first, before undoing multiplication or division.

Examples

  • To solve 4x+5=294x + 5 = 29, first subtract 5 from both sides to get 4x=244x = 24. Then, divide both sides by 4 to find x=6x = 6.
  • To solve y3−2=7\frac{y}{3} - 2 = 7, first add 2 to both sides to get y3=9\frac{y}{3} = 9. Then, multiply both sides by 3 to find y=27y = 27.
  • To solve 18=6+2z18 = 6 + 2z, first subtract 6 from both sides to get 12=2z12 = 2z. Then, divide both sides by 2 to find z=6z = 6.

Explanation

Think of it as reversing your morning routine. To get back to the start, you undo the last thing you did first. In equations, this means handling addition or subtraction before dealing with multiplication or division to isolate the variable.

Section 2

Solving Two-Step Equations with Fractions

Property

To solve two-step equations containing fractions, we can eliminate the fractions first by multiplying both sides by the least common denominator (LCD). This creates an equivalent equation without fractions that follows the standard two-step solving process.

Steps to solve two-step equations with fractions:

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Equations with Two Operations

Property

To solve an equation with two or more operations, we must isolate the variable on one side of the equation. We undo the operations in reverse order. Typically, we undo addition or subtraction first, before undoing multiplication or division.

Examples

  • To solve 4x+5=294x + 5 = 29, first subtract 5 from both sides to get 4x=244x = 24. Then, divide both sides by 4 to find x=6x = 6.
  • To solve y3−2=7\frac{y}{3} - 2 = 7, first add 2 to both sides to get y3=9\frac{y}{3} = 9. Then, multiply both sides by 3 to find y=27y = 27.
  • To solve 18=6+2z18 = 6 + 2z, first subtract 6 from both sides to get 12=2z12 = 2z. Then, divide both sides by 2 to find z=6z = 6.

Explanation

Think of it as reversing your morning routine. To get back to the start, you undo the last thing you did first. In equations, this means handling addition or subtraction before dealing with multiplication or division to isolate the variable.

Section 2

Solving Two-Step Equations with Fractions

Property

To solve two-step equations containing fractions, we can eliminate the fractions first by multiplying both sides by the least common denominator (LCD). This creates an equivalent equation without fractions that follows the standard two-step solving process.

Steps to solve two-step equations with fractions: