Solve one-step and multistep linear equations in one variable. | Linear equations in one variable | SAT Math

Use inverse operations in reverse order to isolate the variable, then check your answer.

Core Idea

Use inverse operations in reverse order — undo addition/subtraction first, then undo multiplication/division — to isolate the variable.

Understanding

A one-step equation needs just one operation to solve: $𝑥 + 5 = 12$ is solved by subtracting 5 from both sides. A multistep equation needs two or more operations.

For multistep equations, reverse the order of operations. If the equation is $3 𝑥 + 7 = 22$ , the variable was first multiplied by 3, then had 7 added. Undo in reverse: subtract 7 first, then divide by 3.

When fractions or decimals appear, you can clear them early by multiplying every term by the LCD (least common denominator). This turns a messy-looking equation into one with whole numbers.

Step by Step

Simplify each side of the equation if needed (distribute, combine like terms).
Use inverse operations to undo addition or subtraction — move constant terms away from the variable.
Use inverse operations to undo multiplication or division — isolate the variable completely.
Check your answer by substituting it back into the original equation.

Misconceptions

Forgetting to apply an operation to both sides of the equation — subtracting from the left but not the right.
Dividing only the first term by the coefficient instead of every term on both sides.
Reversing the order of operations incorrectly — trying to divide before subtracting when the variable term has both.

Question

Worked Example

What is the solution to $4 𝑥 - 9 = 23$ ?

Select an answer to see the explanation