Mathematics

Solving Linear Equations: The Balancing Act

An intuitive look at solving equations by treating them as balanced scales, using inverse operations to isolate the unknown variable.

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The Balance Scale Intuition

3x + 7 = 22

Think of an equation as a perfectly balanced scale. What we do to one side, we must do to the other to keep that balance.

Step-by-step solver

(a) Start with equation

Identify the initial state of the problem.

3x + 7 = 22

(b) Subtract 7

Subtract 7 from both sides to begin isolating the term with x.

3x + 7 - 7 = 22 - 7

Calculate the results of the subtraction on both sides.

3x = 15

(d) Divide by 3

Divide both sides by the coefficient of x, which is 3, to find the value of x.

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

(e) Solve

The final value of x.

x = 5

(f) Check

Substitute 5 back into the original equation to verify the result.

3(5) + 7 = 15 + 7 = 22

Original question

Solve the equation 3x + 7 = 22 and explain each step.

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