What you’ll learn
Rearrange formulas for a target variable.
Key idea
Undo the added prior segment first, then divide by the nonzero rate; apply each inverse operation to both sides.
Undo added segment before nonzero rate division; keep literal formula structure and time units, rejecting stray operators or variable substitutions.
Worked example
Enter the exact value or ordered values in the format requested below.
Supplied distance model D=4+rt: D is total kilometers, 4 km is a prior segment, r is later km/hour and t is hours, r≠0. Isolate t symbolically as an equation in D and r; do not enter a numerical example.
- Supplied D=4+rt: subtract prior distance 4 from both sides, obtaining D-4=rt.
- Divide by nonzero r to isolate t=(D-4)/r. At D=16 km,r=6 km/hour, t=(16-4)/6=2 hours.
Answer: t=(D-4)/r
Quick Check
Evaluate a worked attempt at rearrange formulas for a target variable, identify the first invalid step, and provide the correction.
Supplied distance model D=5+rt: D is total kilometers, 5 km is a prior segment, r is later km/hour and t is hours, r≠0. Step 1 notes that 5 is added to rt. Step 2 adds it again and claims t=(D+5)/r. Locate the first invalid inverse operation and repair the formula.