📖 What IS a Literal Equation?
- A literal equation has MORE THAN ONE variable — like a formula you rearrange!
- Examples: A = l×w (area) | d = r×t (distance) | y = mx+b (slope) | C = (5/9)(F−32) (temp)
- Goal: get ONE specific variable ALONE on one side — like solving a puzzle backwards!
STEP 1: Identify
- Find which variable
- you are solving FOR
- Circle it!
- e.g. Solve for r
- in: d = r × t
STEP 2: Isolate
- Get that variable ALONE
- Use OPPOSITE operations:
- + → subtract both sides
- × → divide both sides
- Work from OUTSIDE in!
STEP 3: Check!
- Plug NUMBERS in
- to BOTH versions
- Do you get same answer?
- YES = you're correct!
- NO = check your steps
Solve d = rt for r
- d = r · t
- Divide both sides by t:
- r = d/t
- Check: d=60,t=3 → r=20 ✓
Solve A=(1/2)bh for h
- Multiply both sides by 2:
- 2A = b·h
- Divide by b:
- h = 2A/b
Solve y=mx+b for m
- y = mx + b
- Subtract b: y−b = mx
- Divide by x:
- m = (y−b)/x
Solve P=2l+2w for w
- P = 2l + 2w
- Subtract 2l: P−2l = 2w
- Divide by 2:
- w = (P−2l)/2
Balance Scale Rule
- Whatever you do to ONE side, do the EXACT SAME to the OTHER side to keep it balanced!
- Add to one side? Add same to other. Divide one side? Divide the other too.
- This is the SECRET of all algebra — every step keeps the equation perfectly balanced!
🔢 Desmos Strategies
3 Ways to Get the Answer!
Strategy 1: Evaluate / Find a Value
- CAPITAL letters to CHECK
- Original: type D = R * T
- Add sliders D, R, T
- Set D=60, T=3 → R must = 20
- Rearranged: type R = D/T
- Set D=60,T=3 → also R=20! Match!
Strategy 2: Graph / Visualize
- Graph both forms to VERIFY
- type y = 2*x + 4 (original)
- Solve for x: x=(y−4)/2
- Intercepts reveal formula values
- Mostly use Strategy 1 for literal eq.
- Graph confirms correctness!
Strategy 3: Generate Table
- Use Table to verify formula
- Test original AND rearranged
- e.g. d=rt: r=3,t=4 → d=12
- Rearranged r=d/t: d=12,t=4→r=3
- Same values = formula is correct!
- Table is your proof!
Remember This!
- Work BACKWARDS! Last thing done = first thing to undo. Like unwrapping a present in reverse.
- Whatever you do to one side, do the EXACT SAME to the other side. Every single time!
- ALWAYS check with real numbers: plug into both forms of the equation to confirm they match.