Q53. - Algebra 1

Question

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

Step-by-Step Solution

Answer

Yes, p = -3 is a solution of 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.

$-5+2p=-11$ Original equation

Substitute -3 for p.

$\Rightarrow -5+2(-3)=-11$

Multiply 2 by -3 in the second term of the equation.

$$\begin{gathered} \Rightarrow -5-6=-11 \\ \Rightarrow -11=-\mathrm{11...} \text{True} \end{gathered}$$

Therefore, p = -3 is a solution of $\mathbf{-}\mathbf{5}\mathbf{+}\mathbf{2}\mathit{p}\mathbf{=}\mathbf{-}\mathbf{11}$.