Model equations using a balance

A balance model interprets an equation as two expressions with equal value: each side represents a total, and a variable represents an unknown quantity whose value makes the totals equal. It illustrates that adding, subtracting, multiplying, or dividing both sides by the same nonzero number preserves equality, whereas changing only one side generally does not. The focus is one-variable linear equations with integer or rational quantities, not systems or nonlinear equations.

Detailed Explanation: Model equations using a balance

Think of an equation as a balanced scale. The left side and right side have the same value:

3x+4=19

The left side is $3x+4$ , and the right side is $19$ . The variable $x$ represents an unknown number.

To find $x$ , keep the balance by doing the same operation to both sides.

Remove the $4$ .
Since $4$ is added to $3x$ , subtract $4$ from both sides:

3x+4-4=19-4

This gives:

3x=15

Find the value of one $x$ .
The expression $3x$ means $3$ groups of $x$ . Divide both sides by $3$ :

\frac{3x}{3}=\frac{15}{3}

So:

x=5

Check the answer.
Substitute $5$ for $x$ in the original equation:

3(5)+4=19

15+4=19

The equation is true, so the solution is:

\boxed{x=5}

Adding, subtracting, multiplying, or dividing both sides by the same nonzero number keeps the equation balanced. Changing only one side would change the balance.

Learn by doing: Model equations using a balance

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Algebra Weights - 2 Scales, 1 Shape, to Equation

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Model equations using a balance

Detailed Explanation: Model equations using a balance

Learn by doing: Model equations using a balance

Practice with unlimited practice problems

Practice:

Algebra Weights - 2 Scales, 1 Shape, to Equation