Which of these is NOT a linear equation in one variable?

Class 8Linear Equations in One VariableLinear Equations

A $\frac{x}{2} + 3 = 7$
B $0.4 x = 1.2$
C $5 x - 4 = 2 x$
D $\frac{2}{x} + 3 = 7$

Step-by-Step Solution

In a linear equation the variable appears only to the first power and never in a denominator.

\frac{2}{x}

has

x

in the denominator, so that one is not linear.

\frac{x}{2}

is perfectly linear — there the variable is simply multiplied by

\frac{1}{2}

, which is the trap most students fall into here.

Answer: D)

\frac{2}{x} + 3 = 7

Key idea: The five-step recipe

For any linear equation in one variable, follow this order:

1. **Open brackets** if any (use distributive property).
2. **Clear fractions** by multiplying both sides by the LCM of all denominators.
3. **Move all variable terms to one side**, all constants to the other (transposition — flip signs).
4. **Combine like terms** on each side.
5. **Divide** both sides by the coefficient of the variable.

Then **verify** by substituting back into the original equation. Always.

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