Q5. - Algebra 1

Question

MULTIPLE CHOICE Solve $\frac{d+5}{10}=2$

A. 10        B. 15        C. 20        D. 25

Step-by-Step Solution

Answer

Option B is correct.

Step 1. Definition and Some properties.

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. Apply Multiplication Property of Equality.

$\begin{array}{l}\frac{d+5}{2}=2 \mathrm{Original} \mathrm{Equation}\\ \Rightarrow \frac{d+5}{2}\times 10=2\times 10 \mathrm{Multiply} \mathrm{both} \mathrm{sides} \mathrm{by} 10\end{array}$

Using Multiplication Property of Equality, multiplying 10 on both sides, we want to cancel out the denominator 10 on the left-hand sides of the original equation

Step 3. Apply Addition Property of Equality.

$\Rightarrow d+5=20$

Using, Addition Property of Equality, subtract 5 on both sides.

$\Rightarrow d+5-5=20-5 \mathrm{Subtract} 5 \mathrm{from} \mathrm{both} \mathrm{sides}.$

$\Rightarrow d=15$

Thus, Option B is correct.