This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the equalities from the diagram. The diagram shows three segments marked with a single tick. This indicates that these three segments have equal lengths. The lengths are given by the expressions (2x-1), (2y+1), and (y-3). Therefore, we can set up the following equations: 2x - 1 = y - 3 (Equation 1) 2y + 1 = y - 3 (Equation 2) Step 2: Solve for y using Equation 2. Equation 2 only contains the variable y, so we can solve it directly: 2y + 1 = y - 3 Subtract y from both sides of the equation: 2y - y + 1 = -3 y + 1 = -3 Subtract 1 from both sides of the equation: y = -3 - 1 y = -4 Step 3: Substitute the value of y into Equation 1 to solve for x. Now that we have the value of y, substitute y = -4 into Equation 1: 2x - 1 = y - 3 2x - 1 = (-4) - 3 2x - 1 = -7 Add 1 to both sides of the equation: 2x = -7 + 1 2x = -6 Divide by 2: x = (-6)/(2) x = -3 The value of x is -3.