-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
B. subtract 15x from both sides of the equation and then simplify
C. subtract 24 from both sides of the equation and then simplify
The correct options are A and C.
A. Combine like terms 15x and 16x to get 31x and then subtract 31x from both sides of the equation:
-15x + 24 + 16x = 3x - 24
31x + 24 = 3x - 24
31x - 3x + 24 = -24
28x + 24 = -24
C. Subtract 24 from both sides of the equation and then simplify:
28x + 24 = -24
28x = -24 - 24
28x = -48
Note that these steps lead to an equation in the form x = a, where a is a number, showing that the equation has one solution.
To transform the equation into the form x = a, where a is a number, you need to isolate the variable x on one side of the equation. Here are the steps that can be used:
1. Combine like terms 15x and 16x to get 31x.
This step can be achieved by adding the coefficients of x on the left side of the equation: -15x + 16x = x.
2. Combine the constant terms 24 and -24 on the right side of the equation to simplify it.
This can be done by adding the constant terms on both sides: 24 - 24 = 0.
3. Subtract 3x from both sides of the equation and then simplify.
To get the variable term x alone on one side of the equation, you subtract 3x from both sides: x - 3x = -3x.
4. Subtract 24 from both sides of the equation and then simplify.
To further isolate the variable x, you subtract 24 from both sides: 0 - 24 = -24.
The two options that apply to achieve the desired form x = a are:
B. Subtract 15x from both sides of the equation and then simplify.
C. Subtract 24 from both sides of the equation and then simplify.
So, options B and C are the correct choices.