Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36
Step 1: Distribute the 3 to the terms inside the parentheses.
3x - 12 + 5x = 9x - 36
Step 2: Combine like terms on the left side of the equation.
8x - 12 = 9x - 36
Step 3: Subtract 8x from both sides to isolate the x term on the right side.
-12 = x - 36
Step 4: Add 36 to both sides to isolate the x term on the left side.
24 = x
So the solution to the equation is x = 24.
A Subtraction Property of EqualitySubtraction Property of Equality
B Commutative Property of AdditionCommutative Property of Addition
C Addition Property of EqualityAddition Property of Equality
D Additive Inverse Property
To solve the equation "3(x - 4) + 5x = 9x - 36," follow these steps:
Step 1: Distribute
Apply the distributive property by multiplying 3 to both terms within the parentheses, resulting in: 3x - 12 + 5x = 9x - 36.
Step 2: Combine Like Terms
Combine the like terms on each side of the equation. On the left side combine 3x and 5x to get 8x. The equation becomes: 8x - 12 = 9x - 36.
Step 3: Move Variables
Move all the x terms to one side of the equation. Subtract 8x from both sides to isolate the x term: -12 = 9x - 8x - 36.
Simplifying this equation further results in: -12 = x - 36.
Step 4: Move Constants
Move the constants (in this case, -36) to the other side of the equation by adding 36 to both sides: -12 + 36 = x - 36 + 36.
Simplifying this equation further results in: 24 = x.
Therefore, the solution to the given equation is x = 24.
To solve the given equation, we will follow the steps below:
Step 1: Distribute the 3 to the terms inside the parentheses.
The equation becomes: 3x - 12 + 5x = 9x - 36
Step 2: Combine like terms on both sides of the equation.
On the left side, we have 3x + 5x = 8x, and on the right side, we have 9x - 36.
So the equation simplifies to: 8x - 12 = 9x - 36
Step 3: Isolate the variable terms on one side of the equation.
Let's subtract 8x from both sides:
8x - 8x - 12 = 9x - 8x - 36
This gives us: -12 = x - 36
Step 4: Isolate the x-term on one side of the equation.
To do this, we need to add 36 to both sides:
-12 + 36 = x - 36 + 36
This simplifies to: 24 = x
Therefore, the solution to the equation 3(x - 4) + 5x = 9x - 36 is x = 24.