Question

Solve each equation.

$\mathbf{6}\mathit{k}\mathbf{+}\mathbf{(}\mathbf{3}\mathbf{·}\mathbf{10}\mathbf{-}\mathbf{8}\mathbf{)}\mathbf{=}\mathbf{(}\mathbf{2}\mathbf{·}\mathbf{3}\mathbf{)}\mathit{k}\mathbf{+}\mathbf{22}$

Short answer

There is no solution to this equation.

Step-by-step solution

Step 1. Definition.

Equation: An equation is a mathematical statement that two expressions are equal. An equation will always contain an equal sign with an expression on each side.

Step 2. Order of Operations.

BODMAS

B – Brackets First

O – Orders (i.e. Powers and Square Roots etc.)

D – Division

M – Multiplication

A – Addition

S – Subtraction

Step 3. Apply BODMAS Rule.

$6k+(3·10-8)=(2·3)k+22$Original equation

Multiply 3 by 10 on the left side and 2 by 3 on the right side of the equation.

$\Rightarrow 6k+(30-8)=6k+22$

Subtract 8 from 30 on the left side of the equation.

$\Rightarrow 6k+22=6k+22\mathrm{...}\text{True.}$

No matter what value is substituted for u, the left side of the equation will always be equal to the right side. So, the equation will always be true.