What is the solution set of the following equation?
-8x + x + 15 = -7x + 12
{all reals}
Ø
{1/7}
There is no solution. Adding 7x to both sides eliminates the x's.
To find the solution set of the given equation, we can start by simplifying both sides of the equation.
Simplifying the left side:
-8x + x + 15 = -7x + 12
Combining like terms:
-7x + 15 = -7x + 12
Now, let's subtract -7x from both sides of the equation to isolate the terms with x on the right side:
-7x + 15 - (-7x) = -7x + 12 - (-7x)
Simplifying the right side:
-7x + 15 + 7x = -7x + 12 + 7x
The -7x and +7x terms cancel each other out on the right side, leaving us with:
15 = 12
However, this equation is not true. When both sides are equal, we have a true equation, but when the sides are not equal, we have a false equation.
Therefore, the solution set for this equation is an empty set, represented by the symbol Ø.
To find the solution set of the equation -8x + x + 15 = -7x + 12, we need to solve for x.
1. Start by simplifying the equation. Combine like terms on both sides of the equation.
-8x + x + 15 = -7x + 12
(-8x + x) + 15 = (-7x) + 12
-7x + 15 = -7x + 12
2. Move all terms involving x to one side of the equation. In this case, subtract -7x from both sides.
-7x + 15 -(-7x) = -7x + 12 -(-7x)
-7x + 15 + 7x = -7x + 12 + 7x
15 = 12
3. After simplifying the equation further, we can see that 15 is not equal to 12.
4. Since the equation is not true, there are no values of x that satisfy the equation. Hence, the solution set is empty, denoted as Ø.