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Solving One Step Linear Equations

The how to solve an equation page introduced the concept of solving linear equations in Math.

Linear equations can actually be classed depending on their form, the most basic linear equations to solve are called “one step equations” and “two step equations”.
The name refers to the number of steps or sums that need to be performed in order to solve for the given variable in the equation.

This page will follow on from what was shown in the how to solve equations introduction page by showing examples of solving one step linear equations.

An equation such as    x + 3 = 4     is a one step equation.

As it can be solved in one step, which is subtracting  3  from both sides.

This will get the variable  x  by itself on one side of the equals sign, which will give us its the value, and thus solve the linear equation.

x + 3 \space {\text{–}} \space 3 \space = \space 4 \space {\text{–}} \space 3     =>     x = 1

On this occasion it was a step of subtraction that was needed, but as we’ll see, other operations can be the step required for solving.

Solving One Step Linear Equations,


Solve    x \space {\text{–}} \space 2 = 6.


In this example, an addition of  2  to both sides will give us a solution.

x \space {\text{–}} \space 2 + 2 \space = \space 6 + 2
x \space = \space 8


Solve    3x = 18.


Dividing both sides by  3  will get the variable by itself on the left side of the equals, giving a solution.

{\frac{3x}{3}} \space = \space {\frac{18}{3}}
  x \space = \space 6


Solve    \frac{a}{5} = 4.


Multiplication by  5  is the step required for examples such as this one.

\frac{a}{5} \times \space 5 \space = \space 4 \times 5

\frac{5a}{5} \space = \space 20     ,     a \space = \space 20


Solve    \frac{3}{4}b  =  12.


A division by the fraction  \frac{3}{4}  is required here.

This isn’t something to be caught out by, to divide by a fraction we simply flip it upside down, then multiply by this new flipped fraction.

\frac{3}{4}b  ×  \frac{4}{3}   =   12 ×  {\frac{4}{3}}

b  =  \frac{48}{3}     ,     b  =  16

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