Question

geometry support unit 1—introduction to geometry

1. given: 6x − 4 = 3x + 8.

prove: x = 4
(table with columns: statement, reason; handwritten entries include \6x - 4 = 3x + 8\, \addition\ etc.)

Explanation:

Step1: Subtract \(3x\) from both sides

To isolate the variable terms, we subtract \(3x\) from each side of the equation \(6x - 4 = 3x + 8\). This gives us \(6x - 3x - 4 = 3x - 3x + 8\), which simplifies to \(3x - 4 = 8\).

Step2: Add 4 to both sides

Next, we add 4 to both sides of the equation \(3x - 4 = 8\) to isolate the term with \(x\). So, \(3x - 4 + 4 = 8 + 4\), which simplifies to \(3x = 12\).

Step3: Divide by 3

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

Answer:

\(x = 4\) is proven as shown in the steps above.