Questions: 7x + 13 = 3x - 10 + 2x + 23

7x + 13 = 3x - 10 + 2x + 23
Transcript text: $7 x+13=3 x-10+2 x+23$
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Solution

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Solution Steps

To solve the equation \(7x + 13 = 3x - 10 + 2x + 23\), we need to:

  1. Combine like terms on both sides of the equation.
  2. Isolate the variable \(x\) by moving all terms involving \(x\) to one side and constant terms to the other side.
  3. Solve for \(x\).
Step 1: Combine Like Terms

Starting with the equation: \[ 7x + 13 = 3x - 10 + 2x + 23 \] we can combine the terms on the right side: \[ 3x + 2x - 10 + 23 = 5x + 13 \] Thus, the equation simplifies to: \[ 7x + 13 = 5x + 13 \]

Step 2: Isolate the Variable

Next, we isolate \(x\) by moving all terms involving \(x\) to one side and constant terms to the other side: \[ 7x - 5x = 13 - 13 \] This simplifies to: \[ 2x = 0 \]

Step 3: Solve for \(x\)

Dividing both sides by 2 gives: \[ x = 0 \]

Final Answer

\(\boxed{x = 0}\)

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