Q&A for How to Solve Equations with Variables on Both Sides

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  • Question
    How do I solve 6z = -54?
    Community Answer
    Solving for z, you would divide -54 by six to get singular z, with the end result being z=-9.
  • Question
    How do I solve 3y + 9 = 9x -18? It's hard for me because they're two different variables.
    Donagan
    Top Answerer
    You solve for either variable in terms of the other variable (meaning that y will be equal to some expression with x in it, or that x will be equal to some expression with y in it). In this problem you could start by subtracting 9 from both sides of the equation, giving you 3y = 9x - 27. Then to solve for y, divide both sides of the equation by 3. To solve for x instead, first add 27 to both sides of the equation and then divide by 9.
  • Question
    How would I solve 3y + 9 = 9x - 18?
    Donagan
    Top Answerer
    Decide whether you want to solve for x in terms of y or vice versa. If solving for x, divide both sides of the equation by 9. That gives you (y/3) + 1 = x - 2. Add 2 to both sides: (y/3) + 3 = x. If solving for y, divide both sides by 3, which gives you y + 3 = 3x - 6. Subtract 3 from both sides: y = 3x - 9.
  • Question
    In variables on both sides, are there inverse operations when you move them to one side?
    Donagan
    Top Answerer
    When you perform any operation on one side of an equation, you must perform exactly the same operation on the other side too.
  • Question
    How do I solve an equation that has the same variable on both sides?
    Donagan
    Top Answerer
    You would perform a specific operation (add, subtract, multiply, or divide) to both sides of the equation in such a way that the variable would disappear from one side.
  • Question
    How do I ind x if the variable on both sides is the same?
    Donagan
    Top Answerer
    See Method 1 above.
  • Question
    How can I solve 3x+7=14+3x?
    Community Answer
    Subtract 3x from both sides to get 7 = 14. Now there isn't a variable on either side! What value of x makes 7 = 14? None of them because 7 is never equal to 14, so your equation has no solutions.
  • Question
    I am just a primary 6 student and I don't understand the methods above. Can anyone tell me what is 48 * y / 1.6 = 24 * x?
    Donagan
    Top Answerer
    First simplify as much as possible. 24x is already as simple as it can get. 48y / 1.6 simplifies to 30 y (by dividing 48 by 1.6). So 30 y = 24x. Simplify further by dividing both sides of the equation by 6: 5y = 4x. You still have the same equation you started with, but it's in a simpler form. Now you solve for one of the variables in terms of the other variable. To solve for x in terms of y, take the equation 5y = 4x, and divide both sides by 4, so that x = (5y) / 4. To solve for y in terms of x, divide both sides of 5y = 4x by 5, so that y = (4x) / 5. Both answers are correct. You can use either or both.
  • Question
    How can solve 2/y = y/32?
    Donagan
    Top Answerer
    Multiply both sides of the equation by 32y (the product of the two denominators). Thus, (2/y)(32y) = (y/32)(32y). Perform the multiplications, so that 64 = y², and y = +/- 8. Either answer works.
  • Question
    How can I solve 1 - g = [2g - 7/3]?
    Donagan
    Top Answerer
    Add g to both sides, and add 7/3 to both sides. That results in 1 + 7/3 = 3g, which simplifies to 10/3 = 3g. Divide both sides by 3: 10/9 = g.
  • Question
    How would I solve 2a + 15 = 3c if a and c are consecutive integers?
    Donagan
    Top Answerer
    Rewrite the equation substituting (a + 2) for c (since c is 2 greater than a). Thus, 2a + 15 = 3(a + 2) = 3a + 6. Subtract 2a from both sides, and subtract 6 from both sides: 9 = a, and c = 9 + 2 = 11.
  • Question
    How can I solve 19 + 4x = 1 - 5x?
    Community Answer
    First subtract 1 from both sides. 18 + 4x = -5x. Now subtract 4x from both sides: 18 = -9x. Finally, divide both sides by -9: -2 = x.
  • Question
    How can I solve 19 + 4x = 1 - 5x?
    Community Answer
    First subtract 1 from both sides: 18 + 4x = -5x. Now subtract 4x from both sides: 18 = -9x. Finally, divide both sides by -9: -2 = x.
  • Question
    How can I solve 19 + 4x = 1 - 5x?
    I_l1ke_gam3s
    Community Answer
    Subtract 1 from both sides, and add 5x to both sides. You get 18 + 9x = 0. Then subtract 18 from both sides. 9x = -18, and x = -2.
  • Question
    How do I solve 2b+15=5a+b?
    Community Answer
    When you have one equation in two unknowns, all you can do is solve for one variable in terms of the other. If 2b + 15 = 5a + b, subtract b from both sides, leaving b + 15 = 5a. Subtract 15 from both sides to find that b = 5a - 15. That's the only value for b we can get. If we return to b + 15 = 5a, and then divide both sides by 5, we find that a = (b + 15) / 5. Again, that's the only available value for a.
  • Question
    How do you solve 15x -10 = -9x + 2?
    I_l1ke_gam3s
    Community Answer
    Add 9x to both sides. You get 24x - 10 = 2. Now add 10 on both sides: 24x = 12. Divide both sides by 24: x = 12/24 = 1/2.
  • Question
    What if the variables on both sides are the same? For example, 2x + 3 = 2x - 4.
    Community Answer
    If the variable is the same on both sides, the other numbers would have to be the same, too. The example equation you give is not valid, because if you subtract 2x from both sides, you're left with 3 = -4.
  • Question
    How to solve for -2+1=-4+9
    Community Answer
    That's not true. Simplify both sides -2+1=-1, yet -4+9=5 so this would be a false statement and something you couldn't solve.
  • Question
    What does x equal in most equations?
    I_l1ke_gam3s
    Community Answer
    There's not a value that x is "mostly". Even if there was, you can't be 100% sure you know what the value is unless you solve it. But x is rarely zero, so you can eliminate zero if it is an option. However, this isn't recommended either, because you need to solve it to know for sure what the value of x is.
  • Question
    How would I solve: (x+14)/x = 8?
    Community Answer
    Multiply the denominator (x) to both sides; you'd get x+14=8. But then eliminate the x from the original numerator from both sides to get 14=7x. Divide both sides by 7, and you'll get an x value of 2.
  • Question
    Why does the sign sometimes change after distributing?
    Community Answer
    It depends on the signs involved. If you multiply a negative by a positive, you’ll get a negative result, and if you multiply a negative by a negative, you’ll get a positive result.
  • Question
    How do you solve 12÷3(5-1)? It's been driving people crazy on internet video, some say it's 1, some say it's 16. So?...
    Community Answer
    The order of operations is PEMDAS: parentheses, exponents, multiply/divide, add/subtract. 12 ÷ 3 (5 - 1) = 12 ÷ 3 (4). Now you're left with nothing but multiplying and dividing, in which case you work from left to right: 12 ÷ 3 is 4, and (4)(4) = 16.
  • Question
    When you cancel variables, how do you know which side to cancel from?
    Community Answer
    The idea is to isolate a variable on either side of an equation. It doesn't matter which side. You perform whatever operation(s) is necessary to achieve that isolation. For example, let's say you're solving this equation for x: 3x + 3 = 5x - 1. You want to wind up with 1x on either side of the equation. In this case the easiest thing to do is subtract 3x from both sides of the equation to wind up with no x on the left side and 2x on the right side. Then add 1 to both sides to wind up with +4 on the left side and no constant at all on the right side. So we have +4 = 2x. Finally, divide both sides by 2 in order to isolate x on the right side: 2 = x. You could have performed slightly different operations to isolate the x on the left side if you preferred.
  • Question
    Solve 36 + 9x = 18 + 10x
    Community Answer
    Subtract 9x from both sides: 36 = 18 + x. Then subtract 18 from both sides: 18 = x.
  • Question
    How do you solve 8(7 + 3h) = 45?
    Community Answer
    8(7 + 3h) = 56 + 24h = 45. Subtract 56 on both sides: 24h = -11. So h = -11/24.
  • Question
    How would I solve 4y= 2(y-5)-2?
    Community Answer
    4y = (2y - 10) - 2 = 2y - 12. Subtract 2y from both sides. 2y = -12. So y = -6.
  • Question
    How would I solve 3x - 24 = 5x?
    Community Answer
    Subtract 3x from both sides: -24 = 2x. Divide both sides by 2: -12 = x.
  • Question
    How would I solve 7x-5 = 2x+15?
    I_l1ke_gam3s
    Community Answer
    Subtract 2x from both sides and add 5 to both sides. You get 5x = 20. Divide both sides by 5, leaving x = 4.
  • Question
    How do I solve equations with variables on both sides?
    Community Answer
    After simplifying, the first step in solving an equation with a variable on both sides is to get the variable on one side.
  • Question
    How do I solve 12(x-2)+3=1/2(x+6)+2?
    Aiden Chester
    Community Answer
    We need to manipulate the equation to get x by itself. 2(12(x-2))+2(3) = 2(1/2)(x+6)+2(2); 24(x-2)+6 = (x+6)+4 = x+10; 24x-48+6 = 24x-42 = x+6+4 = x+10; 24x-42 = x+10; 23x = 53; therefore, x = 53/23.
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