Solve and justify your answer using the properties of operations (i.e Distributive property, associative property, commutative property, identity property, substitution, ect…)
4.5 - 7 = 2(y + 2.25) + 6.6
To solve the equation 4.5 - 7 = 2(y + 2.25) + 6.6, we will utilize the properties of operations to simplify and calculate the value of y.
First, we distribute the 2 to both terms inside the parentheses: 2(y + 2.25) = 2y + 2(2.25).
Next, we simplify the expression inside the parentheses: 2(2.25) = 4.5.
The equation now becomes: 4.5 - 7 = 2y + 4.5 + 6.6.
We combine like terms: -2.5 = 2y + 11.1.
To isolate the term with y, we subtract 11.1 from both sides: -2.5 - 11.1 = 2y.
Performing the subtraction: -13.6 = 2y.
Finally, we divide both sides of the equation by 2 to solve for y: -13.6 / 2 = y.
Calculating the division: -6.8 = y.
Hence, the solution to the equation 4.5 - 7 = 2(y + 2.25) + 6.6 using the properties of operations is y = -6.8.
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 utilize the properties of operations to simplify and calculate the value of x.
First, we distribute the -3 to both terms inside the parentheses: -3(3 - 2x) = -3 * 3 - (-3 * 2x).
Next, we simplify the expression inside the parentheses: -3 * 3 = -9 and -3 * 2x = -6x.
The equation now becomes: -9 + 6x = -9 - (-6x).
We simplify the double negative by changing the subtraction to addition: -9 + 6x = -9 + 6x.
This equation is an example of the commutative property of addition: changing the order of terms does not affect the result.
Since both sides of the equation are equal, we can conclude that any value of x would satisfy the equation.
Therefore, there are infinitely many solutions for x in the equation -9 + 6x = -3(3 - 2x).
so what is the answer?
Apologies for the confusion. In the equation -9 + 6x = -3(3 - 2x), there is an error in the previous response stating that there are infinitely many solutions for x.
Let's solve the equation correctly:
-9 + 6x = -3(3 - 2x)
First, we distribute the -3 to both terms inside the parentheses: -3(3 - 2x) = -9 + 6x.
The equation now becomes: -9 + 6x = -9 + 6x.
Next, we simplify the equation:
Adding 9 to both sides: -9 + 6x + 9 = -9 + 6x + 9
Simplifying further: 6x = 6x
The equation simplifies to 6x = 6x, which means that the value of x can be any real number.
Therefore, the answer is that there are infinitely many solutions for x in the equation -9 + 6x = -3(3 - 2x).
Solve and justify your answer using the properties of operations (i.e Distributive property, associative property, commutative property, identity property, substitution, ect…)
7(x+4) = 5(x+2)
To solve the equation 7(x + 4) = 5(x + 2), we will utilize the properties of operations to simplify and calculate the value of x.
First, we distribute the 7 and 5 to the terms inside the parentheses: 7x + 28 = 5x + 10.
Next, we can rearrange the equation in order to group like terms:
Subtract 5x from both sides: 7x + 28 - 5x = 5x + 10 - 5x
Simplifying both sides: 2x + 28 = 10
Now, we can isolate the term with x by subtracting 28 from both sides: 2x + 28 - 28 = 10 - 28
Simplifying further: 2x = -18
Lastly, we divide both sides of the equation by 2 to solve for x: 2x/2 = -18/2
Simplifying the division: x = -9
Hence, the solution to the equation 7(x + 4) = 5(x + 2) using the properties of operations is x = -9.
Solve and justify your answer using the properties of operations (i.e Distributive property, associative property, commutative property, identity property, substitution, ect…)
-6y + 8 = y +9 - 7y - 1
To solve the equation -6y + 8 = y + 9 - 7y - 1, we will utilize the properties of operations to simplify and calculate the value of y.
First, we can combine like terms on the right-hand side of the equation: y - 7y = -6y and 9 - 1 = 8.
The equation now becomes: -6y + 8 = -6y + 8.
This equation is an example of the commutative property of addition: changing the order of terms does not affect the result.
Since both sides of the equation are equal, we can conclude that any value of y would satisfy the equation.
Therefore, there are infinitely many solutions for y in the equation -6y + 8 = y + 9 - 7y - 1.