Questions: Solve using the principles together. Don't forget to check. 8 x+48=3 x-12 What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is x= . (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.

$Solve using the principles together. Don't forget to check. 8 x+48=3 x-12 What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is x= . (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.$

Transcript text: Solve using the principles together. Don't forget to check. \[ 8 x+48=3 x-12 \] What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is $x=$ $\square$ . (Type an integer or a simplified fraction.) B. The solution is all real numbers. C. There is no solution.

Solution

Solution Steps

Step 1: Move all $ x $-terms to one side

Subtract $ 3x $ from both sides of the equation: \[ 8x + 48 - 3x = 3x - 12 - 3x \] Simplify: \[ 5x + 48 = -12 \]

Step 2: Move constant terms to the other side

Subtract $ 48 $ from both sides: \[ 5x + 48 - 48 = -12 - 48 \] Simplify: \[ 5x = -60 \]

Step 3: Solve for $ x $

Divide both sides by $ 5 $: \[ \frac{5x}{5} = \frac{-60}{5} \] Simplify: \[ x = -12 \]

Step 4: Check the solution

Substitute $ x = -12 $ into the original equation: \[ 8(-12) + 48 = 3(-12) - 12 \] Simplify: \[ -96 + 48 = -36 - 12 \] \[ -48 = -48 \] The solution is correct.