Question

Determine whether the given number is a solution to the equation.

$\mathbf{6}\mathbf{+}\mathbf{4}\mathit{m}\mathbf{=}\mathbf{18}\mathbf{;}\mathbf{3}$

Short answer

Yes, m = 3 is a solution of the given 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.

Solve Equations: A mathematical statement that contains algebraic expressions and symbols is an open sentence. A sentence that contains an equals sign =, is an equation.

A value for a variable that makes a sentence true is called, solving the open sentence.

This replacement value is a solution.

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.

$6+4m=18$Original equation

Substitute 3 for m.

$\Rightarrow 6+4\left(3\right)=18$

Multiply 4 by 3 in the second term of the equation.

$\Rightarrow 6+12=18$

Add 6 and 12.

$\Rightarrow 18=\mathrm{18...}\text{True}$

Therefore, m = 3 is a solution of $\mathbf{6}\mathbf{+}\mathbf{4}\mathit{m}\mathbf{=}\mathbf{18}$.