Q51. - Algebra 1

Question

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

$\mathbf{3}\mathit{r}\mathbf{+}\mathbf{7}\mathbf{=}\mathbf{-}\mathbf{5}\mathbf{;}\mathbf{2}$

Step-by-Step Solution

Answer

No, r = 2 is not a solution to the given equation.

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.

$3r+7=-5$ Original equation

Substitute 2 for r.

$\Rightarrow 3\left(2\right)+7=-5$

Multiply 2 by 3 in the first term of the equation.

$\Rightarrow 6+7=-5$

Add 6 and 7.

$\Rightarrow 13=-5\mathrm{....}\text{False}$

Therefore, r = 2 is not a solution of $\mathbf{3}\mathit{r}\mathbf{+}\mathbf{7}\mathbf{=}\mathbf{-}\mathbf{5}$.