By Sandra Parker | Updated August 30, 2022

Solving algebraic equations comes down to a single principle: finding the unknown. The key is that whatever operation you perform on one side of the equation must be mirrored on the other, keeping the balance intact. Once the equation is balanced, a series of arithmetic steps will isolate the variable and reveal its value.

Step 1: Simplify the Equation

Start by reducing the equation to its most straightforward form. Removing extraneous operations such as square roots or exponents cuts complexity. For instance, the equation 2t – 29 = 7 is already in its simplest state and ready for manipulation.

Step 2: Isolate the Variable

The goal is to get the variable (here, t) on one side and a single number on the other: t = (…). This requires performing identical operations on both sides. If you add 29 to the left side to eliminate the subtraction, add the same 29 to the right side to keep the equation balanced:

2t – 29 = 7
2t – 29 + 29 = 7 + 29
2t = 36

Step 3: Complete the Isolation

Divide both sides by 2 to solve for t:

2t / 2 = 36 / 2
t = 18

Now the equation is solved.

Step 4: Verify Your Solution

Plug the value back into the original equation to confirm it satisfies the equality:

2(18) – 29 = 7
36 – 29 = 7
7 = 7

The left‑hand side equals the right‑hand side, confirming the solution is correct.

What You’ll Need

• An algebraic equation
• Calculator (optional but helpful)
• Paper and pencil

TL;DR

Keep the equation balanced by mirroring every operation on both sides; the remainder is a series of arithmetic steps that isolate the unknown.