Algebra Question of the Day

1. $y = \dfrac{c - ax}{b}$ (correct answer)
2. $y = \dfrac{c}{ab} - x$
3. $by = c - a$
4. $y = \dfrac{ax - c}{b}$

Explanation: This question tests your ability to rearrange formulas with multiple variables—an essential skill for working with formulas in science, geometry, and real life. Rearranging formulas (sometimes called solving literal equations) works exactly like solving regular equations, with one difference: instead of finding a number, we're finding a formula that expresses one variable in terms of the others. The same algebraic moves apply—we just keep the variables as letters instead of substituting numbers! To solve ax + by = c for y, we first subtract ax from both sides: by = c - ax. Then we divide both sides by b: y = (c - ax)/b. Choice A is correct because it properly isolates y using subtraction of ax and division by b, giving y = (c - ax)/b. Perfect! Choice B incorrectly shows y = (ax - c)/b, which has the wrong sign—we subtract ax from c, not c from ax. Choice C tries to separate the fraction incorrectly, forgetting that we need to divide the entire expression (c - ax) by b. The secret to rearranging formulas: pretend the variable you want to solve for is x (like in regular equations), and treat all the other variables like they're numbers. Use the same steps—add, subtract, multiply, divide, just like normal! For example, solving ax + by = c for y is like solving 3 + 2y = 11 for y: subtract 3 (or ax), then divide by 2 (or b). Common formula rearrangements to practice: d = rt becomes t = d/r (divide by rate) and r = d/t (divide by time); A = lw becomes l = A/w (divide by width); P = 2l + 2w becomes l = (P - 2w)/2 (subtract 2w, divide by 2). The same formulas show up repeatedly in math and science, so learning these rearrangements once helps you many times!