➕ Algebra 1 · Equations
Equations with Variables on Both Sides flashcards
Say the answer out loud before you flip. Cards you miss come back sooner; cards you know come back later. That spacing is what builds long-term memory.
All 14 flashcards at a glance
Card 1
What is the goal when the variable is on both sides?
Gather all the variable terms on one side and all the plain numbers on the other, using the same move on both sides.
Card 2
Solve 9x − 5 = 4x + 20.
x = 5. Subtract 4x: 5x − 5 = 20. Add 5: 5x = 25. Divide by 5.
Card 3
In 11x + 4 = 6x + 19, how do you remove the 6x from the right side?
Subtract 6x from both sides to get 5x + 4 = 19 (which gives x = 3).
Card 4
Solve 15 − 2x = x − 6.
x = 7. Add 2x to both sides: 15 = 3x − 6. Add 6: 21 = 3x. Divide by 3.
Card 5
The variables cancel and you are left with a true statement like 5 = 5. What does that mean?
Every number is a solution: infinitely many solutions.
Card 6
The variables cancel and you are left with a false statement like 2 = 9. What does that mean?
There is no solution. No number makes the equation true.
Card 7
You get 0 = 0 while solving. Is the solution x = 0?
No. 0 = 0 is true no matter what x is, so every number is a solution. x = 0 is only one of them.
Card 8
How many solutions does 3(x + 1) = 3x + 3 have?
Infinitely many. Distributing makes the left side 3x + 3, the same as the right side.
Card 9
How many solutions does 2x + 5 = 2x − 1 have?
None. Subtract 2x from both sides to get 5 = −1, which is false.
Card 10
Solve x/3 + 5 = x/2 + 1.
x = 24. Multiply every term by 6: 2x + 30 = 3x + 6. Subtract 2x: 30 = x + 6. So x = 24.
Card 11
Solve 4(x − 2) = x + 7.
x = 5. Distribute: 4x − 8 = x + 7. Subtract x: 3x − 8 = 7. Add 8: 3x = 15. Divide by 3.
Card 12
How do you check a solution when the variable is on both sides?
Substitute it into the original equation and work out each side separately. Both sides must give the same number.
Card 13
Why is it allowed to subtract a variable term from both sides?
Doing the same thing to both sides keeps the equation balanced, so the solution does not change.
Card 14
In this lesson’s STAND memory trick, what do the letters stand for?
Simplify each side, Take the variable terms to one side, Add or subtract the plain numbers, Now divide by the coefficient, Double-check in the original.