Lesson 4 of 1524
Solving a linear equation
Do the same thing to both sides until the letter stands alone.
Practice this chapterAn equation says two expressions are equal. If you add, subtract, multiply, or divide on the left, do the same on the right.
Undo addition with subtraction. Undo multiplication with division.
The letter can start on either side. You are finished when you have one letter equal to one number.
A two-step equation
ax + b = c → x = (c − b) / a
Subtract b, then divide by a.
Worked example
Solve 3x + 6 = 21.
- 1The 6 is added onto 3x. Subtract 6 from both sides so the two sides stay equal: 3x + 6 − 6 = 21 − 6.
- 2That simplifies to 3x = 15.
- 3x is multiplied by 3. Divide both sides by 3: x = 15 / 3 = 5.
- 4Check by putting 5 back into the original equation: 3(5) + 6 = 15 + 6 = 21. Both sides match.
Result: x = 5
Why. Subtracting 6 undoes the addition, and dividing by 3 undoes the multiplication. The check works because 3 × 5 + 6 really is 21, so 5 is the number the equation describes.
Dividing only the term next to x, and not the whole other side, breaks the equation.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.