given: Qs=42 prove: x=13

Question

Statements 1. QS=42 2. QR+RX=QS 3. (X+3)+2X=42 4. 3X+3=42 5. 3x=39 6. X=13 Fill-in-the-blanks: Reasons 1. 2. Segment addition postulate 3. 4. 5. 6. Division property of equality

Answer 1

(X+3)+2X=42=QS; QR+RX=QS, so QR=X+3 and 2X=RX. Therefore, starting at (3) we get to (4) by expanding the brackets and collecting the X terms together. Then in (5) we subtract 3 from each side and in (6) we divide each side by 3 to get X=13. We can work out QR=13+3=16 and RX=2*13=26, so that 16+26=42=QS. This demonstrates the addition property between bracketed and I bracketed expressions and between like terms (X terms). The division property is demonstrated by the final division between (5) and (6).