Solve and justify your answer using the properties of operations (i.e Distributive property, associative property, commutative property, identity property, substitution, ect…)
-9 + 6x = -3(3 - 2x)
To solve the equation -9 + 6x = -3(3 - 2x), we will use the properties of operations to simplify and isolate the variable x.
First, let's distribute -3 to the terms inside the parentheses on the right-hand side of the equation:
-3(3 - 2x) = -9 + 6x
The equation now becomes -9 + 6x = -9 + 6x. We have a special case where both sides of the equation contain the same expression.
To further simplify this equation, we can add 9 to both sides:
-9 + 6x + 9 = -9 + 6x + 9
6x = 6x
The equation now becomes 6x = 6x. We haven't solved for x yet, but we have an equation where both sides are equal.
Now let's subtract 6x from both sides:
6x - 6x = 6x - 6x
0 = 0
The equation becomes 0 = 0. This equation is true for all real numbers. It means that any value of x will satisfy the equation.
Therefore, the solution to the equation -9 + 6x = -3(3 - 2x) is x belongs to the set of real numbers.
To solve the equation -9 + 6x = -3(3 - 2x), we will use the properties of operations step by step. The goal is to isolate the variable x on one side of the equation.
Step 1: Distributive Property
-3(3 - 2x) simplifies to -9 + 6x. The equation becomes -9 + 6x = -9 + 6x.
Step 2: Combine Like Terms
We have the same terms on both sides of the equation (-9 and 6x). So, the equation can be rewritten as 0 = 0.
Step 3: Commutative Property
Since the equation 0 = 0 is true for any value of x, we can say that x can take on any value.
Step 4: Identity Property
The identity property states that for any number a, a + 0 = a. In this case, 0 = 0 satisfies the identity property.
Therefore, the solution to the equation -9 + 6x = -3(3 - 2x) is x can be any real number.
To solve the equation -9 + 6x = -3(3 - 2x) using the properties of operations, we will apply step-by-step operations.
Step 1: Simplify the equation using the distributive property.
Distribute -3 to (3 - 2x) on the right side of the equation:
-9 + 6x = -3 * 3 + (-3) * (-2x)
Step 2: Simplify the equation further.
-9 + 6x = -9 + 6x
Step 3: Combine like terms on each side.
The equation now becomes:
-9 + 6x = -9 + 6x
Step 4: Commutative property (optional).
Since both sides of the equation are the same, we can rearrange the terms without affecting the solution. In this case, we can switch the terms on each side:
-9 + 6x = 6x - 9
Step 5: Subtract 6x from both sides.
-9 + 6x - 6x = 6x - 9 - 6x
-9 = -9
Step 6: The equation simplifies to -9 = -9.
The equation is satisfied for any value of x. Therefore, the solution for this equation is all real numbers.