Question

geometry support unit 1—intro 4. given: 6x − 4 = 3x + 8. prove: x = 4

Explanation:

Step1: Add 4 to both sides

To isolate the terms with \( x \), we first add 4 to both sides of the equation \( 6x - 4 = 3x + 8 \). This gives us \( 6x - 4 + 4 = 3x + 8 + 4 \), which simplifies to \( 6x = 3x + 12 \).

Step2: Subtract \( 3x \) from both sides

Next, we subtract \( 3x \) from both sides to get all the \( x \)-terms on one side. So, \( 6x - 3x = 3x + 12 - 3x \), which simplifies to \( 3x = 12 \).

Step3: Divide both sides by 3

Finally, we divide both sides by 3 to solve for \( x \). That is, \( \frac{3x}{3} = \frac{12}{3} \), which gives \( x = 4 \).

Answer:

\( x = 4 \) is proven.