Variable

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.

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. How do I do this.?(Math.)

    Use the Substitution method to solve the system of equations. y - 2x = -5 3y - x = 5 Solve one of the equations for x or y. Let's solve the first one for y: y - 2x = -5 y = 2x - 5 Now let's substitute 2x - 5 for y in the second

  2. Physics

    You are given vectors A = 5.0i - 6.5j and B = -2.5i + 7.0j. A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of C with B is 15.0. Find the x and y components to vector C. Here's

  3. Algebra

    Create a system of equations that includes one linear equation and one quadratic equation. Part 1. Show all work to solving your system of equations algebraically. Part 2. Graph your system of equations, and show the solution

  4. Math

    Lesson 8: Systems of Linear and Quadratic Equations Check my work 1. Solve the system of equations. y = 2x^2 - 3 y = 3x - 1 a. no solution b. (-1/2, 5), (2, -5/2) c. (-1/2, -5/2), (2,5)*** d. (1/2, 5/2), (2, 5) 2.how many real

  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

  2. Algebra22222!!!

    Choose the ordered pair that is a solution to the system of equations. 3x - y = 10 -x + y = -4 (3, -7) (-1, 3) (3, -1) (3, 1) Follow the example I gave in your previous question. I'm not going to do all of them. You want to

  3. Please Math

    8. p + 4 < –24 p < –20 p < 28 p < –28 p < 20 9.p/8 ≥ –5 p ≥ 40 p ≥ 3 p ≥ –13 p ≥ –40 10. –5p > –30 p > 6 p < 6 p > –35 p < 35 11. Which inequality matches the graph? 3x + 1 > 4 3x + 1 ≥ 4 3x + 1 < 4

  4. math

    Please explain in detail how to solve each question: At a certain high school, 350 students are taking an algebra course. The ratio of boys to girls taking algebra is 33:37. How many more girls are taking algebra than boys? How

  1. Math

    Write the equations described below. a) an addition equation with one variable that has a solution of 3 b) a subtraction equation with one variable that has a solution of 2/3

  2. Math

    Which of the following is not a strategy for solving simple exponential equations? Question 12 options: a) Express both sides as powers with a common base and then equate the exponents. b) Divide both sides by the common base and

  3. Finite Math

    Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions involving one parameter, enter the solution using t for the last

  4. Math

    1. Which ordered pair is a solution of the equation y = −11x + 4? a. (0, -7) b. (-1, -7) c. (1, -7) d. (2, 26) MY ANSWER: C Because (X,Y) so -11x = -11 * 1 = -11 -11 + 4 = -7 2. A plumber charges $65 per hour to fix a leak. What

You can view more similar questions or ask a new question.