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Solve 2(x + 3) = 14 (Step by Step)

How to solve the equation 2(x + 3) = 14 with brackets, step by step, two ways, with a quick check of the answer.

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

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Step-by-step solution

Q

Solve 2(x + 3) = 14

A
  1. Start with the equation: 2(x + 3) = 14.
  2. Divide both sides by 2 to undo the × 2: (x + 3) = 14 ÷ 2, so x + 3 = 7.
  3. Subtract 3 from both sides to undo the + 3: x + 3 − 3 = 7 − 3, so x = 4.
  4. Check your answer: put x = 4 back in. 2(4 + 3) = 2(7) = 14. Both sides match, so x = 4 is correct. ✓

Answer: x = 4

Q

Another way: multiply out the bracket first

A
  1. Multiply the 2 by each term inside the bracket: 2 × x + 2 × 3 = 14, so 2x + 6 = 14.
  2. Subtract 6 from both sides: 2x = 8.
  3. Divide both sides by 2: x = 4.
  4. Same answer as before. Check: 2(4) + 6 = 8 + 6 = 14. ✓

Answer: x = 4

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Frequently asked questions

Should I divide first or multiply out the bracket first?

Either works. Dividing by 2 first is quicker here because 14 divides evenly by 2. Multiplying out the bracket always works, even when the numbers do not divide evenly.

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

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

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