Solve multi-step equations

Key Notes:

What Are Multi-Step Equations?

• Definition: Equations that require two or more operations (addition, subtraction, multiplication, or division) to isolate the variable.
• Example: 3x+7=16 (needs subtraction and division to solve).

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Steps to Solve Multi-Step Equations

Step 1: Simplify both sides

• Remove parentheses using Distributive Property:
  a(b+c)=ab+ac
• Combine like terms (terms with the same variable or constants).

Step 2: Move variable terms to one side

• Use Addition or Subtraction Property of Equality:
  If a=b, then a+c=b+c and a−c=b−c.

Step 3: Move constant terms to the other side

• Get constants on one side and variables on the other.

Step 4: Isolate the variable

• Use Multiplication or Division Property of Equality:
  If a=b, then a⋅c=b⋅c or a/c​=b/c​ (where c≠0).

Step 5: Check your solution

• Substitute the value back into the original equation.

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Example Problems with Solutions

Example 1:

2(x+3)−4=10

Solution:

1. Distribute: 2x+6−4=10
2. Combine like terms: 2x+2=10
3. Subtract 2 from both sides: 2x=8
4. Divide by 2: x=4
5. Check: 2(4+3)−4=14−4=10 ✔

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Example 2:

5x−7=3x+9

Solution:

1. Subtract 3xfrom both sides: 2x−7=9
2. Add 7 to both sides: 2x=16
3. Divide by 2: x=8
4. Check: 5(8)−7=33✔

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Example 3 (Fractions):

x/3+4=7

Solution:

1. Subtract 4: x/3=3
2. Multiply by 3: x=9
3. Check: 9/3+4=3+4=7 ✔

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Tips & Tricks

• Always simplify first before moving terms.
• If you see parentheses, distribute before anything else.
• Keep the variable positive when possible for easier solving.
• Check your answer to avoid mistakes.

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Practice Questions

Solve each:

1. 4(x−2)=20
2. 3x+5=2x+9
3. 2×5−4=6
4. 7−2(x−3)=1
5. 5x−3=2x+12

To solve for a variable, use inverse operations to undo the operations in the equation. Be sure to do the same operation to both sides of the equation.

Learn with an example

let’s practice!