Questions: Solve and check the following equation. 3x-5=7+2x

Transcript text: Solve and check the following equation. \[ 3 x-5=7+2 x \]

Solution

Solution Steps

To solve the equation \(3x - 5 = 7 + 2x\), we need to isolate the variable \(x\). We can do this by first moving all terms involving \(x\) to one side of the equation and constant terms to the other side. Then, we solve for \(x\) and check the solution by substituting it back into the original equation.

Step 1: Move all terms involving \( x \) to one side

Starting with the equation: \[ 3x - 5 = 7 + 2x \] Subtract \( 2x \) from both sides to get: \[ 3x - 2x - 5 = 7 \] This simplifies to: \[ x - 5 = 7 \]

Step 2: Isolate \( x \)

Add 5 to both sides to isolate \( x \): \[ x - 5 + 5 = 7 + 5 \] This simplifies to: \[ x = 12 \]

Step 3: Check the solution

Substitute \( x = 12 \) back into the original equation to verify: \[ 3(12) - 5 = 7 + 2(12) \] Simplify both sides: \[ 36 - 5 = 7 + 24 \] \[ 31 = 31 \] Since both sides are equal, the solution is verified.

Final Answer

\[ \boxed{x = 12} \]

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