Solve the following equation. You must show all your work and list the correct properties for each step to receive full credit.
(here are the possible properties to pick from: addition property of equality, subtraction property of equality, multiplication property of equality, division property of equality)
x/3 − 4 =6
Starting with the equation:
x/3 - 4 = 6
First, we need to isolate x/3 by adding 4 to both sides of the equation using the addition property of equality:
x/3 - 4 + 4 = 6 + 4
x/3 = 10
Next, we need to isolate x by multiplying both sides of the equation by 3 using the multiplication property of equality:
3 * (x/3) = 3 * 10
x = 30
Therefore, the solution to the equation x/3 - 4 = 6 is x = 30.
Properties Used:
- addition property of equality
- multiplication property of equality
To solve the given equation, let's apply the following properties step by step:
1. Addition Property of Equality: We can add the same number to both sides of an equation without changing its solution.
Let's start by adding 4 to both sides of the equation to isolate the term with "x":
(x/3) - 4 + 4 = 6 + 4
This simplifies to:
x/3 = 10
2. Multiplication Property of Equality: We can multiply both sides of an equation by the same number without changing its solution.
Next, we want to get rid of the fraction by multiplying both sides of the equation by 3:
3 * (x/3) = 3 * 10
This simplifies to:
x = 30
Therefore, the solution to the equation x/3 - 4 = 6 is x = 30.
The properties used in this solution are the Subtraction Property of Equality and the Multiplication Property of Equality.
To solve the equation x/3 - 4 = 6, we will follow these steps:
Step 1: Add 4 to both sides of the equation to isolate the x/3 term.
(addition property of equality)
(x/3 - 4) + 4 = 6 + 4
x/3 = 10
Step 2: To get rid of the fraction, multiply both sides of the equation by 3.
(multiplication property of equality)
3 * (x/3) = 10 * 3
(3/1) * (x/3) = 30/1
(3 * x) / (3 * 3) = 30
x/1 = 30
x = 30
Therefore, the solution to the equation x/3 - 4 = 6 is x = 30.