Variable

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    A=1/2h (b1 + b2) Solve for b1 A=1/2h (b1 + b2) Solve for b1 I assume this is A = (1/2)(h)(b1 + b2); i.e., the h is in the numerator and not the denominator Multiply both sides by 2. 2A = (2*1/2)h(b1 + b2). 2*1/2 on the right side is …
  2. math

    how do you solve 9x=6 9x=6 Divide both side by 9. (Remember you can add, subtract, multiply, etc but do to both sides what you do to one.) 9x/9 = 6/9 The 9's divide out on the left leaving x. x = 6/9. I will let you reduce the answer. …
  3. algebra--distributive

    how would you do this prob. negative4-(5y+6) = negative 7y+3 thanks. happy halloween I'm going to assume your problem is this: -4 - (5y + 6) = -7y + 3 If that's the case, distribute the negative over the terms in the parentheses first: …
  4. Algebra

    I don't understand how to do this problems: Solve for the variable r, C=2PIr (PI is the pi symbol thing then r is next to it) and this problem solve for the variable l, S=B+1/2Pl please help :) When you solve for a variable, you want …
  5. Algebra

    - 20> 8 +7a Solve inequalities like you would an equation, EXCEPT if you multiply or divide by a negative number, reverse the inequality sign. Let's look at your problem: - 20 > 8 + 7a First subtract 8 from both sides (whatever …
  6. Pre Cal

    6-x=2x+9 If you are to solve the equation for x, first try to get the variable on one side of the equation. Let's subtract 2x from both sides to start (whatever operation you do to one side of an equation you must do to the other side …
  7. MATH PLEASE CHECK IT!!2

    m-2/m-5*m+5/m-2=-1 If your problem is this: (m - 2)/(m - 5) * (m + 5)/(m - 2) = -1 (m - 2) cancels out in both the numerator and denominator on the left-hand side since you are multiplying. That leaves us with this: (m + 5)/(m - 5) …
  8. math--pre alg

    not sure i did right 3(f+2)+9=13+5f 3f+6+9 = 13+5f +9 3F+15 = 12+5F GOT MIXED UP SOMWERE HELP 3f +6 +9 = 13 + 5f 3f + 15 = 13 + 5f 2f = 2 f = 1 drwls is correct You are doing OK up to this point: 3f + 6 + 9 = 13 + 5f Now combine any …
  9. algebra

    I need a step by step explanation on how to add these two equations 2x+3y=1 5x+3y=16 Subtract the first equation from the second. (Subtract left and right sides separately). This gives you 3x = 15 Then divide both sides by 3. x = 5 …
  10. Math

    I am really have a tough time trying to solve this problem. I think my first three steps are correct but I am not sure. Could someone please help me?

More Similar Questions