3(x + 4) = 21 has the bracket multiplied by 3.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Route one: divide first
Divide both sides by 3 to get x + 4 = 7, so x = 3.
Route two: expand first
3x + 12 = 21, so 3x = 9 and x = 3.
Which to use
Divide first when the division is clean. Expand first when it is not.
Two valid routes
For 3(x + 4) = 21, you can divide both sides by 3 first, giving x + 4 = 7 and then x = 3. Or expand first: 3x + 12 = 21, so 3x = 9 and x = 3. Both are correct; the first is quicker when the division is clean.
Choosing between them
Divide first when the number outside divides the right-hand side neatly. Expand first when it does not — for 3(x + 4) = 20, dividing gives x + 4 = 20/3, which is uglier than expanding. Look at the numbers before deciding.
Expanding means everything inside
3(x + 4) is 3x + 12, not 3x + 4. The multiplier applies to every term in the brackets. This is the single most common error in the topic, and it is caught instantly by substituting a test value.
A negative outside the bracket
−2(x − 5) = 4 expands to −2x + 10 = 4. Every term inside gets multiplied by −2, including the sign. Going slowly through each term, rather than trying to do it in one glance, is what keeps this reliable.
Step 2: Try It Yourself
Tap and try it out.
7 + 7 + 7 = 21
3 × 7 = 21
3 × 7 = (3 × 3) + (3 × 4) = 9 + 12 = 21
The array is cut into 3 × 3 and 3 × 4. Two easier facts that add to the same total.
Step 3: Watch an Example
One step at a time.
Watch Leo Try Both Routes
Leo solves 5(x − 2) = 35 two ways.
- Step 1
Dividing first: x − 2 = 7, so x = 9.
Step 4: Your Turn
Practice makes it stick.
The Bracket
Problem 1 of 2
2(x + 3) = 14. What is x?
The Other Route
Problem 2 of 2
4(x − 1) = 20. What is x?
Bracket Equations
1 of 4
3(x + 2) = 18. What is x?
2 of 4
5(x + 1) = 30. What is x?
3 of 4
2(x − 5) = 8. What is x?
4 of 4
Expand 3(x + 4). What is the number term?
Step 5: Quick Check
Show what you know.
Question 1 of 1
6(x + 2) = 42. What is x?
What You Learned
- An equation with a bracket can be divided first or expanded first.
- Divide first when the division comes out clean.
- Both routes must give the same answer.