Examples of multi-step linear equations with distributive property

📚 Quick Study Guide

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• Distributive Property: $a(b + c) = ab + ac$
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• Combining Like Terms: Simplify expressions by adding or subtracting terms with the same variable and exponent.
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• Isolating the Variable: Use inverse operations (addition, subtraction, multiplication, division) to get the variable alone on one side of the equation. Remember, what you do to one side, you must do to the other!
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• Multi-Step Process:
  1. Apply the distributive property to remove parentheses.
  2. Combine like terms on each side of the equation.
  3. Use inverse operations to isolate the variable.
  4. Check your solution by substituting it back into the original equation.
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• Example: $2(x + 3) - 5 = 11$
  • Distribute: $2x + 6 - 5 = 11$
  • Combine like terms: $2x + 1 = 11$
  • Subtract 1 from both sides: $2x = 10$
  • Divide both sides by 2: $x = 5$

✍️ Practice Quiz

1. What is the first step in solving the equation $3(x - 2) = 9$?
   1. Subtract 3 from both sides.
   2. Divide both sides by 3.
   3. Apply the distributive property.
   4. Add 2 to both sides.


2. Solve for $x$: $4(x + 1) = 20$
   1. $x = 4$
   2. $x = 6$
   3. $x = 5$
   4. $x = 7$


3. Simplify: $2(3x - 1) + 4x = ?$
   1. $10x - 2$
   2. $10x + 2$
   3. $6x - 2$
   4. $2x - 2$


4. Solve for $x$: $5(x - 2) + 3 = 8$
   1. $x = 3$
   2. $x = 1$
   3. $x = 5$
   4. $x = 2$


5. What is the value of $x$ in the equation $-(x + 5) = -12$?
   1. $x = 7$
   2. $x = -7$
   3. $x = 17$
   4. $x = -17$


6. Solve: $6 - 2(x + 1) = 10$
   1. $x = -3$
   2. $x = 3$
   3. $x = -1$
   4. $x = 1$


7. Find $x$: $7(2x - 3) - 5x = 23$
   1. $x = 4$
   2. $x = 5$
   3. $x = 6$
   4. $x = 7$