how do you solve these problems?
1.2x/3 + 1/3 - x/8= 2/3
2. 3n + 9/10 + n/5= -2 3/10
3. 3k/4 - 28 - 2k/3 = 37
#1: Multiply both sides by a common denominator, in this case 24.
So you'll get
24* (2x/3 + 1/3 - x/8) = 24* (2/3 )
16x + 8 - 3x = 16
13x = 8
x = 8/13
#2: Multiply both sides by 10
#3: Multiply both sides by 12.
how do you do number 2. with a mixed number like multiply it by 10
-2 3/10 = -23/10
To solve these problems, we will follow a step-by-step approach. The aim is to simplify the equation and isolate the variable on one side of the equation.
Let's solve each problem step-by-step:
1. 2x/3 + 1/3 - x/8 = 2/3
To simplify the equation, let's eliminate the fractions by finding a common denominator. In this case, the least common denominator (LCD) is 24.
Multiplying the entire equation by 24, we get:
(24)(2x/3) + (24)(1/3) - (24)(x/8) = (24)(2/3)
This simplifies to:
16x + 8 - 3x = 16
Combining like terms, we have:
13x + 8 = 16
Next, let's isolate the variable by subtracting 8 from both sides:
13x = 16 - 8
13x = 8
Finally, divide both sides by 13 to solve for x:
x = 8/13
Hence, the solution to the equation is x = 8/13.
2. 3n + 9/10 + n/5 = -2 3/10
Again, we need to find a common denominator to simplify the equation. The LCD here is 10.
Multiplying both sides of the equation by 10, we get:
(10)(3n) + (10)(9/10) + (10)(n/5) = (10)(-2 3/10)
This simplifies to:
30n + 9 + 2n = -23
Combining like terms gives us:
32n + 9 = -23
Now, let's isolate the variable by subtracting 9 from both sides:
32n = -23 - 9
32n = -32
Finally, divide both sides by 32 to solve for n:
n = -32/32
Simplifying, we have:
n = -1
Therefore, the solution to the equation is n = -1.
3. 3k/4 - 28 - 2k/3 = 37
Similar to the previous problems, let's find a common denominator to simplify the equation. The LCD is 12.
Multiplying both sides by 12, we get:
(12)(3k/4) - (12)(28) - (12)(2k/3) = (12)(37)
This simplifies to:
9k - 336 - 8k = 444
Combining like terms, we obtain:
k - 336 = 444
To isolate the variable, we add 336 to both sides:
k = 444 + 336
k = 780
Therefore, the solution to the equation is k = 780.
By following these steps, you can solve these types of problems.