SBP-Program

f

tw

in

Linear equations in one variable

What is a linear equation in one variable?

This equation

ax + b = c

is called a linear equation in one variable.

The "a" is called a coefficient.

The "x" is called a variable or unknown quantity.

The "b" and "c" are called constants.

Pay particular attention to that the variable x raised to 1

ax = ax1

Any variable must be a power with exponent one in a linear equation.

This equation

ax = b

is a linear equation as well.

The constant c equals zero here.

This equation

ax = 0

is a linear equation.

The constants b and c are equal to zero here.

This equation

x = 0

is a linear equation. The coefficient "a" equals 1

1x = 0

The constants b and c are equal to zero here.

Examples of linear equations

x = 5
5x = 10
7x + 3 = 73
30 - x = 110 - 3x

Note, variables x raised to 1 here.

Is this equation a linear one?

7x + 35 = 73

I see 3 raised to 5 and not to 1.

This equation is a linear one because namely variables must be raised to 1, coefficients and constants do not matter.