Member of an Equation

Member of an Equation
Side of an Equation

The two expressions on either side of an equation.

For example, in the equation 2x + 3 = 5x², the members are the expressions 2x + 3 and 5x².

Key Formula

\underbrace{\text{Left Member}}_{\text{first expression}} \;=\; \underbrace{\text{Right Member}}_{\text{second expression}}

Where:

$\text{Left Member}$ = The expression on the left side of the equals sign (also called the first member)
$=$ = The equals sign, which separates the two members
$\text{Right Member}$ = The expression on the right side of the equals sign (also called the second member)

Worked Example

Problem: Identify the two members of the equation 4x + 7 = 3x − 5, then solve by performing the same operation on both members.

Step 1: Identify the left member (the expression to the left of the equals sign).

\text{Left member: } 4x + 7

Step 2: Identify the right member (the expression to the right of the equals sign).

\text{Right member: } 3x - 5

Step 3: Subtract 3x from both members to keep the equation balanced.

(4x + 7) - 3x = (3x - 5) - 3x \implies x + 7 = -5

Step 4: Subtract 7 from both members.

(x + 7) - 7 = (-5) - 7 \implies x = -12

Answer: The left member is 4x + 7, the right member is 3x − 5, and solving gives x = −12.

Another Example

This example shows that a member can be a single constant like 0, and that rewriting an expression (e.g., factoring) does not change which member it belongs to.

Problem: Identify the members of the equation x² + 6x + 9 = 0. Then explain what each member represents.

Step 1: The left member is the entire expression to the left of the equals sign.

\text{Left member: } x^2 + 6x + 9

Step 2: The right member is the expression to the right of the equals sign. Even a single number counts as an expression.

\text{Right member: } 0

Step 3: Notice the left member can be factored, but it is still one member — the entire expression on that side.

(x + 3)^2 = 0

Step 4: After factoring, the left member is now written as (x + 3)², and the right member is still 0. The equation still has exactly two members.

\text{Left member: } (x+3)^2, \quad \text{Right member: } 0

Answer: The left member is x² + 6x + 9 (equivalently (x + 3)²) and the right member is 0.

Frequently Asked Questions

What is the difference between a member and a term of an equation?

A member is an entire side of the equation — everything to the left or right of the equals sign. A term is one of the individual parts within an expression that are separated by addition or subtraction. For example, in 3x + 5 = 2x − 1, the left member is 3x + 5 (which contains two terms: 3x and 5), while the right member is 2x − 1 (which also contains two terms: 2x and −1).

Why is it important to do the same thing to both members of an equation?

An equation states that its two members are equal. If you add, subtract, multiply, or divide one member by a value without doing the same to the other, the two sides are no longer equal and the equation becomes false. This principle is formalized in the properties of equality (additive and multiplicative), which guarantee balance is preserved.

Can an equation have more than two members?

No. By definition, an equation has exactly one equals sign, which creates exactly two members — a left member and a right member. If you see something like a = b = c, this is typically shorthand for two separate equations: a = b and b = c.

Member of an Equation vs. Term of an Expression

	Member of an Equation	Term of an Expression
Definition	An entire expression on one side of the equals sign	A single component of an expression, separated by + or −
How many per equation?	Exactly 2 (left and right)	Can be many — each member may contain multiple terms
Example in 3x + 5 = 2x − 1	Left member: 3x + 5; Right member: 2x − 1	Terms: 3x, 5, 2x, −1
Also called	Side of an equation	Monomial (if a single term)

Why It Matters

Understanding members of an equation is essential when you apply properties of equality. Every time you solve an equation by adding, subtracting, multiplying, or dividing, you perform that operation on both members simultaneously to maintain balance. Textbooks and teachers frequently say "do the same thing to both sides" — "sides" and "members" mean exactly the same thing here.

Common Mistakes

Mistake: Confusing a member with a term. Students sometimes call individual parts like 3x or 5 the "members" of 3x + 5 = 10.

Correction: The entire expression 3x + 5 is one member (the left member). The parts 3x and 5 are terms within that member. The other member is 10.

Mistake: Performing an operation on only one member of an equation.

Correction: Whatever you do to the left member, you must also do to the right member. For instance, subtracting 5 from just the left member of 3x + 5 = 10 would break the equality. You must subtract 5 from both members: 3x + 5 − 5 = 10 − 5.

Related Terms

Equation — An equation is the structure that contains two members
Expression — Each member of an equation is an expression
Properties of Equality — Rules for operating on both members equally
Additive Property of Equality — Adding the same value to both members
Multiplicative Property of Equality — Multiplying both members by the same value
Term — Individual components within a member
Equals Sign — The symbol that separates the two members