Aim for a positive x
Move the x terms to the side that leaves a positive coefficient to avoid extra sign errors.
Why it works
Subtract 4x to leave 2x on the right.
Solving Equations · Variables on both sides · 4.2
Both sides, negatives.
Same method with negatives — moving an x term may flip a sign. 4x + 1 = 6x − 9 → subtract 4x → 1 = 2x − 9 → +9 → 10 = 2x → x = 5.
See it work.
Watch the method
Both sides with negatives
4x + 1 = 6x − 9 → x = 5.
1
The equation
Solve for x — find the value that makes both sides equal.
2
Collect the x terms
Subtract 6x from both sides to get the x terms together.
3
Move the constant
Subtract 1 from both sides.
4
Divide by the coefficient
Divide both sides by -2 to get x by itself.
Practice until it feels automatic.
Your turn
Solve for x.
Type the value of x — a number or a fraction like 3/2.
streak 0
best 0
…x =
The idea underneath.
From easy to tricky.
Solve 5x + 5 = 4x + 6
1
The equation
Solve for x — find the value that makes both sides equal. 5x + 5 = 4x + 6
2
Collect the x terms
Subtract 4x from both sides to get the x terms together. x + 5 = 6
3
Move the constant
Subtract 5 from both sides. x = 1
4
Read the solution
x is already by itself. x = 1
Solve 5x - 7 = 2x + 14
1
The equation
Solve for x — find the value that makes both sides equal. 5x - 7 = 2x + 14
2
Collect the x terms
Subtract 2x from both sides to get the x terms together. 3x - 7 = 14
3
Move the constant
Add 7 to both sides. 3x = 21
4
Divide by the coefficient
Divide both sides by 3 to get x by itself. x = 7
Solve 5x + 7 = 3x + 9
1
The equation
Solve for x — find the value that makes both sides equal. 5x + 7 = 3x + 9
2
Collect the x terms
Subtract 3x from both sides to get the x terms together. 2x + 7 = 9
3
Move the constant
Subtract 7 from both sides. 2x = 2
4
Divide by the coefficient
Divide both sides by 2 to get x by itself. x = 1
Where students slip.
Trap
Creating a negative coefficient needlessly.
Fix
Move x to the side with more of it.
Trap
Losing a sign while moving terms.
Fix
Subtract carefully from both sides.
Test yourself.
The Test
12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.
0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so
t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).Core
Core (4)
C1
Solve 6x + 4 = 2x + 28
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
C2
Solve 4x - 3 = 3x - 4
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
C3
Solve 5x - 7 = 1x + 13
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
C4
Solve 5x + 1 = 4x - 3
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
Apply
Apply (4)
A1
Solve 5x - 6 = 3x + 2
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
A2
Solve 5x + 7 = 2x + 16
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
A3
Solve 3x + 8 = 2x + 3
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
A4
Solve 7x + 4 = 4x + 1
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
Extension
Extension (4)
E1
Solve 6x - 1 = 5x + 2
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
E2
Solve 4x - 8 = 3x - 12
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
E3
Solve 6x - 6 = 5x - 10
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.
E4
Solve 6x - 4 = 1x - 24
Need a hint?
- Move x to keep its coefficient positive.
- Then finish the two-step.