How does an equation balancer work?

It models equations as physical scales. Performing actions like subtracting values on one side requires doing the same on the other to maintain balance.

What is the goal of solving a linear equation?

The goal is to isolate the variable (x) on one side of the equation to find its value.

Linear Equation Balancer - weight scale visualizer

Left Weight Expression3x + (4)

Right Weight Expression1x + (10)

Calculated Solution (x) x = 3

Variable Adjuster

Left Variable Coefficient (a)3

110

Left Constant Term (b)4

-1015

Right Variable Coefficient (c)1

010

Right Constant Term (d)10

-1015

Linear Equation Balancer

EQBAL

An equation represents a balanced scale. To find the unknown value x, we perform the same mathematical operations on both sides (addition, subtraction, multiplication, or division) to isolate x while keeping the scale balanced.

ax + b = cx + d \implies (a-c)x = d-b

Whiteboard Solver Steps

Step 1

Original Equation (Scale Setup)

We begin with our scale in equilibrium: the left pan holds 3 variable boxes of unknown weight $x$ plus a constant weight of 4 units, while the right pan holds 1 variable boxes of weight $x$ plus a constant weight of 10 units.

3x + 4 = 1x + 10

Step 2

Consolidate Variables (Simplify Pans)

To simplify, we remove the smaller amount of variable boxes ( $1x$ ) from both pans. This keeps the scale balanced while concentrating all variable boxes on the left pan: $2x + 4 = 10$ .

\begin{aligned}(3x - 1x) + 4 = 10 \\ 2x + 4 = 10\end{aligned}

Step 3

Isolate Variable Term

Next, we subtract the constant weight of $4$ from both sides. This isolates the variable boxes on the left pan by removing all constant weights from it, leaving: $2x = 6$ .

\begin{aligned}2x = 10 - 4 \\ 2x = 6\end{aligned}

Step 4

Divide to Find Single x Box Weight

Finally, since $2$ boxes of weight $x$ balance a total constant weight of $6$ , we divide the constant weight by the number of boxes. This determines that each individual box $x$ must weigh exactly $3$ units.

x = \frac{6}{2} = 3

RV Anveshana