Question

what are the order the steps for solving the equation: 2x−5=3(4x+5)

Answer 1

To solve the equation \(2x - 5 = 3(4x + 5)\), you can follow these steps in order:

1. **Distribute**: Distribute the \(3\) on the right side of the equation.
\[
2x - 5 = 12x + 15
\]

2. **Move variables to one side**: Subtract \(12x\) from both sides to get all the \(x\) terms on one side.
\[
2x - 12x - 5 = 15
\]
\[
-10x - 5 = 15
\]

3. **Move constant terms to the other side**: Add \(5\) to both sides to isolate the \(x\) term.
\[
-10x = 20
\]

4. **Solve for \(x\)**: Divide both sides by \(-10\) to find the value of \(x\).
\[
x = -2
\]

5. **Check your solution**: It's good practice to substitute the value of \(x\) back into the original equation to verify that it satisfies the equation.
\[
2(-2) - 5 = 3(4(-2) + 5)
\]
\[
-4 - 5 = 3(-8 + 5)
\]
\[
-9 = 3(-3)
\]
\[
-9 = -9
\]

Since both sides are equal, the solution \(x = -2\) is correct.

Thus, the order of steps is:
1. Distribute
2. Move variables to one side
3. Move constant terms to the other side
4. Solve for \(x\)
5. Check the solution