Look at the equation shown.
-15x + 24 + 16x = 3x - 24
What is a step that can be used to transform the equation into the form x = a where a is a number, to show that the equation has one solution? Select TWO options that apply.
A. combine like terms 15x and 16x to get 31x and then subtract 31x from both sides of the equation.
B. Subtract 15x from both sides of the equation and then simplify.
C. Subtract 24 from both sides of the equation and then simplify.
D. Add 3x to both sides of the equation and then simplify.
E. Add 24 to both sides of the equation and then simplify.
Options C and E apply.
C. Subtract 24 from both sides of the equation and then simplify.
-15x + 24 + 16x - 24 = 3x - 24 - 24
Simplifying, we get:
-15x + 16x = 3x - 48
D. Add 24 to both sides of the equation and then simplify.
-15x + 24 + 16x + 24 = 3x - 24 + 24
Simplifying, we get:
-15x + 16x = 3x
To transform the equation into the form x = a where a is a number, you want to isolate the variable x on one side of the equation. Here are the steps that can be used to achieve this:
A. Combine like terms 15x and 16x to get 31x and then subtract 31x from both sides of the equation.
This step involves combining the x terms on one side of the equation and isolating the variable x. However, this step alone is not sufficient to transform the equation into the form x = a.
B. Subtract 15x from both sides of the equation and then simplify.
Subtracting 15x from both sides of the equation helps in getting rid of the term -15x. This step moves the x terms to one side, but further steps are needed to fully isolate x.
C. Subtract 24 from both sides of the equation and then simplify.
Subtracting 24 from both sides of the equation eliminates the constant term on the right side of the equation. This step helps simplify the equation further.
D. Add 3x to both sides of the equation and then simplify.
Adding 3x to both sides of the equation helps in moving the x terms to one side of the equation. This step is important to fully isolate the variable x.
E. Add 24 to both sides of the equation and then simplify.
Adding 24 to both sides of the equation eliminates the constant term on the left side of the equation. This step simplifies the equation further.
The correct steps to transform the equation into the form x = a are options B and E. By subtracting 15x and subtracting 24, you can isolate the variable x on the left side of the equation, and then by adding 24, you simplify further to get the final form x = a.
The correct options are B. Subtract 15x from both sides of the equation and then simplify, and C. Subtract 24 from both sides of the equation and then simplify.
Here's the step-by-step process:
-15x + 24 + 16x = 3x - 24
Subtract 15x from both sides:
(-15x + 24 + 16x) -15x = (3x - 24) - 15x
Simplify:
24 + 16x = 3x - 15x - 24
Combine like terms on the right side:
24 + 16x = -12x - 24
Subtract 24 from both sides:
24 + 16x - 24 = -12x - 24 - 24
Simplify:
16x = -12x - 48
Now the equation is in the form x = a where a is a number.