Step 1 of 10
Start
Read the entire coefficient before choosing an inverse operation.
Demo equation
−4x = 28
−6y = −42
−8n = 56
Unpack
›
Split
›
Flip sign
›
Check
Read the coefficient
−4x=28
−4
Negative four is attached to x by multiplication. The inverse must undo the whole coefficient.
The minus sign belongs to the coefficient. It is not decoration, and it cannot be dropped.
Unpack both sides into four identical bays
Four negative-x tiles have the same total value as twenty-eight positive counters.
negative-x tilespositive counters
−x
=
−x
=
−x
=
−x
=
−4x=4 × 7 = 28
÷ 4 equal bays on both sides
−x = 7
Use the sign press on both sides
Taking the opposite of both sides keeps the equation equal.
× (−1) on both sides
−x
before
x
after
=
+7
before
−7
after
x = −7
Compress both ideas into one inverse operation
Dividing by −4 splits into four groups and flips the sign in one move.
÷ (−4) on both sides
−4x
−4
=
28
−4
x = −7
Substitute −7 back into the original equation
A solution is only finished when the original equation becomes true.
(−4)(−7)=28
−×−=+
4 × 7 = 28
true ✓ solution verified
Now the right side is negative too
Decide the answer sign before dividing the magnitudes.
−6y = −42
÷ (−6) on both sides
−42 ÷ −6
→
positive
42 ÷ 6 = 7
y = 7
(−6)(7) = −42 ✓
Your turn: isolate n
Divide by the entire coefficient. Keep the sign in your calculation.
Use 56 ÷ (−8), then check by substitution.
✎
Solve on your whiteboard
Show the division on both sides and substitute your value into −8n = 56. Submit when you are ready.
Work submitted. The sign-safe solution is unlocked.
The coefficient controls both size and sign
Use the same one-step move, then verify in the original equation.
inverse÷ (−8) on both sides
divide56 ÷ (−8) = −7
solutionn = −7
check(−8)(−7) = 56 ✓
Reliable rule: divide both sides by the entire coefficient, including its sign. Then substitute to check.