Final answer:
Upon simplifying each equation, only equation (b) 2.2z + 3z = 4.5 - 3.2, simplifies to a true statement with one solution for the variable, yielding z = 0.25.
Step-by-step explanation:
To determine which equation has one solution, we need to simplify and solve each given equation:
- (a) 3u + 40 + 2u = 6u - 30: Combine like terms on the left to get 5u + 40. The equation simplifies to 40 + 30 = u, resulting in u = 70. This has one solution.
- (b) 2.2z + 3z = 4.5 - 3.2: Combine like terms to get 5.2z on the left side. On the right side, 4.5 - 3.2 gives 1.3, and the equation becomes 5.2z = 1.3. Solving for z gives z = 0.25, which is one solution.
- (c) 2.3y + 3.2 - y = 2.1 + 1.3y + 1.1: Combine like terms to get 1.3y + 3.2 on the left side. On the right side, 2.1 + 1.1 gives 3.2, and combining like terms with y gives 1.3y. The equation simplifies to 1.3y + 3.2 = 1.3y + 3.2, which is true for all values of y, thus it has an infinite number of solutions.
- (d) 20 + 41 = 32 - 27: This is not an equation with a variable, it is a simple arithmetic statement. When we simplify both sides, we get 61 = 5, which is not true, meaning this is not a solvable equation with a solution.
Comparing all options, option (b) is the equation that has one solution, z = 0.25.