Q9. - Algebra 1

Question

Solve each equation.

$(2\cdot 5)+\frac{c{}^3}{3}=c^3÷(1^5+2)+10$

Step-by-Step Solution

Answer

The solution to this equation could be any real numbers.

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

Addition Property of Equality

If any two expressions are equal to each other,  If we add the same value to both sides of the equation, the equation will remain equal.

For all real numbers a, b, and c: If a = b, then a + c = b + c.

Since subtraction can be written as an addition (adding the opposite), the addition property of equality can be used for subtraction as well.

Multiplication Property of Equality

If two expressions are equal to each other and you multiply both sides by the same number, the resulting expressions will also be equivalent.

For all real numbers a, b, and c: If a = b, then a • c = b • c (or ab = ac).

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.

$(2\cdot 5)+\frac{c{}^3}{3}=c^3÷(1^5+2)+10$ Original equation

Expand power.

$(2\cdot 5)+\frac{c{}^3}{3}=c^3÷(1+2)+10$

Multiply 2 by 5 on the left side of the equation.

Add 1 and 2 on the right side of the equation.

$\begin{array}{l}\Rightarrow 10+\frac{c{}^3}{3}=c^3÷3+10\\ \Rightarrow 10+\frac{c{}^3}{3}=\frac{c^3}{3}+\mathrm{10....}\mathrm{True}.\end{array}$

No matter what real value is substituted for c, 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 numbers