Question

Solve each equation.

$3^2-2·3+u=(3^3-3·8)\left(2\right)+u$

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.

$3^2-2·3+u=(3^3-3·8)\left(2\right)+u$Original equation

Evaluate powers.

$\Rightarrow 9-2·3+u=(27-3·8)+u$

Multiply 2 by 3 on the left side and 3 by 8 on the right side of the equation.

$\Rightarrow 9-6+u=(27-24)\left(2\right)+u$

Subtract 6 from 9 on the left side and 24 from 27 on the right side of the equation.

$\begin{array}{l}\Rightarrow 3+u=3\left(2\right)+u\\ \Rightarrow 3+u=6+u\mathrm{...}\text{False}\end{array}$

No matter what value is substituted for u, the left side of the equation will be not equal to the right side. So, the equation will always be False.

Therefore, there is no solution to this equation.