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ALGEBRA · EQUATIONS & LINES

Solving Linear Equations

Isolate the variable by doing the same thing to both sides — every time.

12 min read 4 practice questions
An equation is a balance: whatever you do to one side, you must do to the other. A linear equation in one variable can always be written as ax+b=cax + b = c, and solving it means finding the value of xx that makes both sides equal.
The strategy is to undo operations in reverse order. Addition and subtraction come off first, then multiplication and division.
ax+b=c⟹x=c−baax + b = c \quad\Longrightarrow\quad x = \frac{c - b}{a}

The general solution, valid whenever a ≠ 0

Worked example · Variables on both sides

Solve 5x−7=2x+115x - 7 = 2x + 11.
  1. 1
    Subtract 2x2x from both sides: 3x−7=113x - 7 = 11.
  2. 2
    Add 77 to both sides: 3x=183x = 18.
  3. 3
    Divide both sides by 33: x=6x = 6.
  4. 4
    Check: 5(6)−7=235(6) - 7 = 23 and 2(6)+11=232(6) + 11 = 23. ✓

Worked example · Distributing first

Solve 3(x−4)=2x+53(x - 4) = 2x + 5.
  1. 1
    Distribute: 3x−12=2x+53x - 12 = 2x + 5.
  2. 2
    Subtract 2x2x: x−12=5x - 12 = 5.
  3. 3
    Add 1212: x=17x = 17.

CHECK YOUR UNDERSTANDING

Practice

Answer each question, then check.

1
Solve for xx: 4x+9=374x + 9 = 37.
2
Solve for xx: 7x−3=4x+157x - 3 = 4x + 15.
3
Which value solves 2(x+3)=5x−92(x + 3) = 5x - 9?
4
Solve for xx: x3−2=4\dfrac{x}{3} - 2 = 4.

Numeric answers accept decimals or fractions like 3/4.