Expand any brackets before collecting terms. 3(x + 2) = 18 becomes 3x + 6 = 18.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Fractions can be cleared
Multiply every term by the denominator. x/4 + 2 = 5 becomes x + 8 = 20.
Every term, both sides
Multiplying only some terms changes the equation. The 2 has to be multiplied as well as the x/4.
Then it is an ordinary equation
Once brackets and fractions are gone, collect the x terms on one side and solve.
Multiply through to clear fractions
For x/3 + 1/2 = 2, multiply every term by 6, the least common denominator: 2x + 3 = 12. Clearing fractions at the start turns a messy equation into a clean one, and it costs one extra step.
Every term, without exception
The multiplier must be applied to every term on both sides, including any that are already whole numbers. Missing one term is the standard error here, and it produces an equation that is no longer equivalent.
Expand brackets before gathering
Deal with brackets first, then clear fractions, then gather like terms, then solve. Following a fixed order means you are never deciding what to do next, which is where hesitation turns into mistakes.
Check against the original equation
Substitute into the equation as first given, fractions and all. Checking against your cleaned-up version would miss an error made in the clearing step, which is exactly the step most likely to go wrong.
Step 2: Try It Yourself
The bracket drawn as a rectangle, cut into the two products it makes.
6 + 6 + 6 = 18
3 × 6 = 18
3 × 6 = (3 × 2) + (3 × 4) = 6 + 12 = 18
The array is cut into 3 × 2 and 3 × 4. Two easier facts that add to the same total.
Step 3: Watch an Example
One step at a time.
Watch Ana Clear a Fraction
Ana solves x/3 + 4 = 10.
- Step 1
She multiplies every term by 3, including the 4 and the 10.
Step 4: Your Turn
Practice makes it stick.
The Bracket
Problem 1 of 2
4(x + 3) = 32. What is x?
The Fraction
Problem 2 of 2
x/2 + 3 = 9. What is x?
Clear and Solve
1 of 4
2(x + 5) = 24. What is x?
2 of 4
x/5 = 4. What is x?
3 of 4
3(x − 2) = 15. What is x?
4 of 4
x/4 + 1 = 6. What is x?
Step 5: Quick Check
Show what you know.
Question 1 of 1
5(x + 1) = 40. What is x?
What You Learned
- Expand brackets and clear fractions before collecting terms.
- Multiply every term on both sides, not only the fractional one.
- What is left is an ordinary linear equation.