Solving Equations with Unknown Variables

The exam may include questions that ask you to work with an equation that has one or more unknown variables.

We can solve equations that have only one unknown variable.

However, when an equation has two or more unknown variables, we cannot really solve the problem.

Solving Equations with One Unknown Variable

(1) If 3x – 2(x + 1) = 5, then x = ?

A. 3

B. 5

C. 7

D. 13

E. 17

In order to solve algebraic equations with one unknown variable, you have to multiply and then isolate the variable in question.

STEP 1: Perform the multiplication on the parenthetical expression.

Remember to be careful with the negative sign.

3x – 2(x + 1) = 5

3x – 2x – 2 = 5

STEP 2: Then perform any addition or subtraction.

(3x – 2x) – 2 = 5

x – 2 = 5

STEP 3: Deal with the remaining whole number.

x – 2 = 5

x – 2 + 2 = 5 + 2

STEP 4: Isolate the variable to solve the problem

x – 2 + 2 = 5 + 2

x – 0 = 5 + 2

x = 7

So, the correct answer is C.

(2) If x + y − 1 = z – x + 2, then z = ?

A. xy − 1

B. x + y + 1

C. x − y − 1

D. 2x + y − 1

E. 2x + y − 3

To find the answer to questions like this one, we need to get the requested variable on one side of the equation.

The other unknown variables will need to be placed on the other side of the equation.

STEP 1: Deal with the whole numbers first.

First, we want to eliminate the “2” on the right side of the equation.

x + y − 1 = z − x + 2

x + y − 1 − 2 = z − x + 2 − 2

x + y − 3 = z − x

STEP 2: Now isolate z by moving the x to the other side.

x + y − 3 = z − x

x + x + y − 3 = z − x + x

2x + y − 3 = z

z = 2x + y − 3

So, the correct answer is E.