Questions: Solve the equation and check. 8x - 7 = 1 + 6x

Solve the equation and check. 8x - 7 = 1 + 6x
Transcript text: Solve the equation and check. \[ 8 x-7=1+6 x \]
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Solution

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Solution Steps

Step 1: Move all \(x\)-terms to one side and constants to the other

Start by subtracting \(6x\) from both sides of the equation to isolate the \(x\)-terms: \[ 8x - 6x - 7 = 1 \] Simplify: \[ 2x - 7 = 1 \]

Step 2: Solve for \(x\)

Add \(7\) to both sides to isolate the \(x\)-term: \[ 2x = 1 + 7 \] Simplify: \[ 2x = 8 \] Divide both sides by \(2\): \[ x = \frac{8}{2} \] Simplify: \[ x = 4 \]

Step 3: Check the solution

Substitute \(x = 4\) back into the original equation to verify: \[ 8(4) - 7 = 1 + 6(4) \] Simplify: \[ 32 - 7 = 1 + 24 \] \[ 25 = 25 \] The equation holds true, so the solution is correct.

Final Answer

\[ \boxed{x = 4} \]

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