➕ Algebra 1 · Equations
Literal Equations and Formulas: true or false
Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.
All statements and answers
To solve V = IR for R, divide both sides by I (when I ≠ 0).
✓ True. IR means I × R, so dividing both sides by I gives R = V ÷ I. This is Ohm’s law, which links voltage, current and resistance.
Solving 3b − k = m for b gives b = (m + k) ÷ 3.
✓ True. Add k to both sides to get 3b = m + k, then divide the whole side by 3. Check with b = 4 and k = 2: m = 10 and (10 + 2) ÷ 3 = 4.
After solving d = rt for t, the letters d and r are gone from the formula.
✗ False. They are still there. t = d ÷ r has t alone on one side and keeps the other letters on the other side.
You can divide both sides of an equation by a letter without worrying whether that letter could be 0.
✗ False. Dividing by 0 is not allowed. When you divide by a letter, you are assuming it is not 0.
Solving S = 4(a + b) for a gives a = S ÷ 4 − b.
✓ True. This is not an ax + b = c shape: the last thing done to a is multiplying the whole sum by 4, so that comes off first. Divide both sides by 4 to get S ÷ 4 = a + b, then subtract b. (Distributing first, S = 4a + 4b, gives a = (S − 4b) ÷ 4, the same formula.) Check with a = 3 and b = 2: S = 20 and 20 ÷ 4 − 2 = 3.
(a − 6b) ÷ 3 and a − 6b ÷ 3 mean the same thing.
✗ False. With a = 12 and b = 1, the first is (12 − 6) ÷ 3 = 2 but the second is 12 − 2 = 10. In the second, only 6b is divided by 3.
To solve y = ab + a for a, you should factor a out of the right side.
✓ True. ab + a = a(b + 1), so y = a(b + 1) and a = y ÷ (b + 1) (when b + 1 ≠ 0).
Solving 3p − 4q = 12 for q gives q = (3p − 12) ÷ 4.
✓ True. Subtract 3p to get −4q = 12 − 3p, then divide by −4: q = (12 − 3p) ÷ (−4) = (3p − 12) ÷ 4. Check with p = 8: q = 3 and 3(8) − 4(3) = 12.
Solving for a letter in a formula needs a brand-new set of rules, different from solving ordinary equations.
✗ False. It uses the same balance rule and the same inverse operations. The only new thing is that some of the “numbers” are letters.
Solving y = x ÷ 3 + 2 for x gives x = 3y − 2.
✗ False. Subtract 2 to get y − 2 = x ÷ 3, then multiply the whole side by 3: x = 3(y − 2) = 3y − 6. Check with x = 9: y = 5 and 3(5) − 6 = 9.