Chapter 8.2, Problem 71HP

To determine

Write a two − step equation that can be solved using the subtraction property of Equality and the Multiplication property of Equality.

Answer to Problem 71HP

The solution of $\frac{y}{5}+7=18$ is y = 55

Explanation of Solution

Given:

Write a two − step equation that can be solved using the subtraction property of Equality and the Multiplication property of Equality. Show how to use these properties to solve an equation.

Concept Used:

Subtraction Property of Equality 

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

If two expressions are equal to each other, and you subtract the same value to both sides of the equation, the equation will remain equal.

Multiplication Property of Equality: For all real numbers a, b, c, if a = b, then $a·c=b·c$

When you multiply both sides of an equation by the same quantity, you still have equality.

Calculation:

Suppose the equation is: $\frac{y}{5}+7=18$

In the left side 7 is added with $\frac{y}{5}$ , to move 7 from left side to right side, we need to subtraction 7 from both sides.

  $\frac{y}{5}+7-7=18-7\Rightarrow \frac{y}{5}=11$

Now in the next step as 5 is in the denominator, we need to multiply by 5 to both sides.

  $5·\frac{y}{5}=5·11\Rightarrow y=55$

  $[5·\frac{1}{5}=1]$

The solution of $\frac{y}{5}+7=18$ is y = 55 by using Subtraction and Multiplication property of equality.

Thus, the solution of $\frac{y}{5}+7=18$ is y = 55