To determine which step would not be involved in solving the equation [tex]\(5x + 15 + 2x = 24 + 4x\)[/tex], let's break down the process step-by-step:
1. Collect like terms:
On the left side of the equation, we have [tex]\(5x\)[/tex] and [tex]\(2x\)[/tex]. Combine these to simplify:
[tex]\[
5x + 2x + 15 = 24 + 4x
\][/tex]
This gives us:
[tex]\[
7x + 15 = 24 + 4x
\][/tex]
Therefore, collecting like terms is indeed a step in solving the equation.
2. Collect variable terms on one side:
To isolate [tex]\(x\)[/tex], subtract [tex]\(4x\)[/tex] from both sides:
[tex]\[
7x - 4x + 15 = 24
\][/tex]
Simplifying, we get:
[tex]\[
3x + 15 = 24
\][/tex]
Therefore, collecting variable terms on one side is also a necessary step.
3. Isolate the variable:
We need to isolate [tex]\(x\)[/tex] by getting rid of the constant term on the left. Subtract 15 from both sides:
[tex]\[
3x + 15 - 15 = 24 - 15
\][/tex]
This simplifies to:
[tex]\[
3x = 9
\][/tex]
Finally, divide by 3:
[tex]\[
x = 3
\][/tex]
Therefore, isolating the variable is necessary to solving the equation.
4. Use the distributive property:
In the given equation [tex]\(5x + 15 + 2x = 24 + 4x\)[/tex], there is no need for the distributive property, since none of the terms involve a factor that needs to be distributed over an addition or subtraction within a parenthesis.
Therefore, the step which would not be involved in solving the equation [tex]\(5x + 15 + 2x = 24 + 4x\)[/tex] is:
A. Use the distributive property.
