SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES
Solve the equation. Then check your solution.
4x-9 = 7x+12
Just remember that one can add, subtract, multiply, divide, etc but whatever is done to one side must be done to the other side of an equation.
4x - 9 = 7x + 12.
Add 9 to both sides.
4x - 9 + 9 = 7x + 12 + 9.
Combine terms.
4x = 7x + 21.
Now subtract 7x from both sides.
4x - 7x = 7x -7x + 21.
Combine terms.
-3x = 21.
multiply both sides by -1.
-1(-3x) = -1(21).
Perform the operation.
3x = -21.
Divide both sides by 3.
3x/3 = -21/3.
Perform the operation.
x = -7.
To check, substitute -7 for x in the original equation and see if that satisfies th equality.
4x - 9 = 7x + 12.
4(-7) - 9 = 7(-7) + 12.
-28 - 9 = -49 + 12.
-37 = -37.
I hope this helps. If you don't understand anything about the solution, please repost but tell us exactly what you don't understand.
Thank you!!
After you see how this is done, a shortcut may be taken as follows:
To move any term from one side to the other, simply change the sign. That is, 4x - 9 = 7x + 12.
Just move the 9 to the right side but change to +9. Move the 7x to the left side by making it -7. Then combine terms and solve for x.
4x - 7x = 12 + 9
-3x = 21.
Now change the sign on both sides.
3x = -21.
x = -21/3 = -7.
This procedure usually is much quicker than the first one but the first one shows you how it all works.
2006...
To solve the equation 4x - 9 = 7x + 12, you need to isolate the variable x on one side of the equation. Here's a step-by-step explanation of the process:
1. Start with the equation: 4x - 9 = 7x + 12
2. Add 9 to both sides of the equation to get rid of the -9 on the left side:
4x - 9 + 9 = 7x + 12 + 9
This simplifies to: 4x = 7x + 21
3. Subtract 7x from both sides of the equation to move the x terms to one side:
4x - 7x = 7x - 7x + 21
This simplifies to: -3x = 21
4. Multiply both sides of the equation by -1 to change the sign of the -3x term:
-1 * (-3x) = -1 * 21
This simplifies to: 3x = -21
5. Divide both sides of the equation by 3 to solve for x:
3x / 3 = -21 / 3
This simplifies to: x = -7
So the solution to the equation is x = -7.
To check if the solution is correct, substitute -7 back into the original equation:
4(-7) - 9 = 7(-7) + 12
-28 - 9 = -49 + 12
-37 = -37
Since both sides of the equation are equal, the solution is correct.
Additionally, there is a shortcut method available:
1. Start with the equation: 4x - 9 = 7x + 12
2. Move the 9 term to the right side by changing its sign to +9:
4x - 7x = 12 + 9
This simplifies to: -3x = 21
3. Change the sign on both sides of the equation:
3x = -21
4. Solve for x by dividing both sides of the equation by 3:
x = -21 / 3
This simplifies to: x = -7
This shortcut method can save time, but it's important to understand the underlying steps of solving equations to ensure accuracy.