Question

Solve each equation.

$\mathbf{(}\mathbf{3}\mathbf{·}\mathbf{5}\mathbf{)}\mathit{t}\mathbf{+}\mathbf{(}\mathbf{21}\mathbf{-}\mathbf{12}\mathbf{)}\mathbf{=}\mathbf{15}\mathit{t}\mathbf{+}{\mathbf{3}}^{\mathbf{2}}$

Short answer

The solution of this equation could be any real number.

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.

$(3·5)t+(21-12)=15t+3^2$Original equation

Expand power on the right side of the equation.

$\Rightarrow (3·5)t+(21-12)=15t+9$

Multiply 3 by 5 and subtract 12 from 21 on the left side of the equation.

$\Rightarrow 15t+9=15t+9\mathrm{....}\text{True}$

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

So, the equation will always be true.

Therefore, the solution of this equation could be any real number.