An equation is a balance: whatever you do to one side must be done to the other. To isolate x, undo the operations in the opposite order they were applied: addition and subtraction come off before multiplication and division. Then substitute the answer back.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Clear the brackets first
3(x + 2) = 15: distribute to 3x + 6 = 15, then 3x = 9, x = 3. Or divide both sides by 3 first: x + 2 = 5, x = 3. Both are valid; the second is shorter when the right side divides cleanly.
Variables on both sides
5x + 3 = 2x + 12: subtract 2x from both sides, 3x + 3 = 12, then 3x = 9, x = 3. Collect the variable terms on whichever side keeps the coefficient positive; it avoids a sign error later.
Fractions
x/4 + 3 = 7: subtract 3, x/4 = 4, multiply by 4, x = 16. Or clear the fraction first by multiplying everything by 4: x + 12 = 28. Either way, one operation at a time.
Two special outcomes
2(x + 3) = 2x + 6 becomes 6 = 6: true for every x, infinitely many solutions. 2(x + 3) = 2x + 1 becomes 6 = 1: false, no solution. When the variables vanish, the statement left behind decides.
Justify each step
Write the move beside each line: "subtract 5 from both sides", "divide both sides by 3". The justification is what makes the working a proof that x = 5, not just a guess that happens to work.
Always check
Substitute the answer into the original equation, not into a later line. 3(5) + 5 = 20 holds. It costs one line and catches nearly every arithmetic slip.
Step 2: Try It Yourself
Tap and try it out.
Solve 4(x − 2) = 2x + 6
- 14x − 8 = 2x + 6distribute the 4
Step 0 of 4
3x + 5 = 20
3x + 5 balances 20. Take the same off both pans and they stay level, because the same was done to each side.
Step 3: In Real Life
A phone bill
A bill of 47 dollars on a plan of 20 plus 0.05 a text: 20 + 0.05t = 47. Undo the 20, then the 0.05: 540 texts. Every bill is an equation with one unknown.
Step 4: Watch an Example
One step at a time.
Watch Amara Solve 3x + 5 = 20
Amara needs the value of x.
- Step 1
The 5 was added last, so it comes off first: subtract 5 from both sides, leaving 3x = 15.
Step 5: Your Turn
Practice makes it stick.
The Equation
Problem 1 of 2
2x + 7 = 19. What is x?
The Tickets
Problem 2 of 2
Tickets cost $8 each plus a $5 booking fee. A total of $53 buys how many tickets?
Isolate the Variable
1 of 8
x + 9 = 15. What is x?
2 of 8
4x = 28. What is x?
3 of 8
5x − 3 = 22. What is x?
4 of 8
3(x + 2) = 18. What is x?
5 of 8
7x = 4x + 12. What is x?
6 of 8
2x + 3 = 2x + 9. How many solutions?
7 of 8
Put the solving steps for 3x + 5 = 20 in order.
- 1Simplify to 3x = 15.
- 2Divide both sides by 3.
- 3Check by substituting back.
- 4Subtract 5 from both sides.
8 of 8
6x − 4 = 2x + 12. What is x?
Step 6: Quick Check
Show what you know.
Question 1 of 2
4x + 6 = 26. What is x?
Question 2 of 2
The variables cancel and leave 7 = 7. How many solutions?
What You Learned
- An equation is a balance; do the same to both sides, and write the move beside each line.
- Undo operations in the reverse of the order they were applied; clear brackets first.
- Vanishing variables leave either every solution or none.
- Substitute your answer into the original equation every time.