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Solve 3(x − 2) = 15 (Step by Step)

How to solve the equation 3(x − 2) = 15 with brackets, step by step, two ways, with a quick check of the answer.

Here x has 2 taken away, and then the whole bracket is multiplied by 3. You can undo the × 3 first by dividing both sides by 3, or you can multiply out the bracket first. Both ways give the same answer.

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Step-by-step solution

Q

Solve 3(x − 2) = 15

A
  1. Start with the equation: 3(x − 2) = 15.
  2. Divide both sides by 3 to undo the × 3: (x − 2) = 15 ÷ 3, so x − 2 = 5.
  3. Add 2 to both sides to undo the − 2: x − 2 + 2 = 5 + 2, so x = 7.
  4. Check your answer: put x = 7 back in. 3(7 − 2) = 3(5) = 15. Both sides match, so x = 7 is correct. ✓

Answer: x = 7

Q

Another way: multiply out the bracket first

A
  1. Multiply the 3 by each term inside the bracket: 3 × x − 3 × 2 = 15, so 3x − 6 = 15.
  2. Add 6 to both sides: 3x = 21.
  3. Divide both sides by 3: x = 7.
  4. Same answer as before. Check: 3(7) − 6 = 21 − 6 = 15. ✓

Answer: x = 7

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Frequently asked questions

Should I divide first or multiply out the bracket first?

Either works. Dividing by 3 first is quicker here because 15 divides evenly by 3. Multiplying out the bracket always works, even when the numbers do not divide evenly.

What is a common mistake with 3(x − 2)?

Only multiplying the x by 3 and forgetting the 2. The 3 multiplies everything in the bracket, so 3(x − 2) is 3x − 6, not 3x − 2.

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