Gather the x’s
Subtract the smaller x term from both sides so x is on one side only, then finish like a two-step.
Why it works
Move the 2x over to leave 3x.
Solving Equations · Variables on both sides · 4.1
Both sides.
When x appears on both sides, first move the variable terms to one side (subtract the smaller x term from both sides), then solve the two-step equation. 5x − 4 = 2x + 8 → −2x → 3x − 4 = 8 → x = 4.
See it work.
Watch the method
Variables on both sides
5x − 4 = 2x + 8 → 3x − 4 = 8 → x = 4.
1
The equation
Solve for x — find the value that makes both sides equal.
2
Collect the x terms
Subtract 2x from both sides to get the x terms together.
3
Move the constant
Add 4 to both sides.
4
Divide by the coefficient
Divide both sides by 3 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 6x - 4 = 5x - 2
1
The equation
Solve for x — find the value that makes both sides equal. 6x - 4 = 5x - 2
2
Collect the x terms
Subtract 5x from both sides to get the x terms together. x - 4 = -2
3
Move the constant
Add 4 to both sides. x = 2
4
Read the solution
x is already by itself. x = 2
Solve 7x + 4 = 4x + 1
1
The equation
Solve for x — find the value that makes both sides equal. 7x + 4 = 4x + 1
2
Collect the x terms
Subtract 4x from both sides to get the x terms together. 3x + 4 = 1
3
Move the constant
Subtract 4 from both sides. 3x = -3
4
Divide by the coefficient
Divide both sides by 3 to get x by itself. x = -1
Solve 7x - 4 = 5x - 6
1
The equation
Solve for x — find the value that makes both sides equal. 7x - 4 = 5x - 6
2
Collect the x terms
Subtract 5x from both sides to get the x terms together. 2x - 4 = -6
3
Move the constant
Add 4 to 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
Moving constants and variables the same way.
Fix
Get the x terms together first, constants second.
Trap
Subtracting from one side only.
Fix
Subtract the x term 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 + 2 = 2x - 6
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
C2
Solve 7x + 8 = 4x + 23
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
C3
Solve 3x - 1 = 1x + 13
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
C4
Solve 7x - 6 = 5x - 2
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
Apply
Apply (4)
A1
Solve 4x + 8 = 3x + 16
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
A2
Solve 4x + 8 = 1x + 11
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
A3
Solve 6x - 5 = 1x + 15
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
A4
Solve 6x + 8 = 5x + 7
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
Extension
Extension (4)
E1
Solve 3x + 8 = 1x + 10
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
E2
Solve 5x + 5 = 3x - 3
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
E3
Solve 4x + 6 = 3x + 9
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.
E4
Solve 5x - 1 = 2x + 23
Need a hint?
- Subtract the smaller x term from both sides.
- Then solve the two-step.