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
thank you can you please show me step by step how you got the answer?
I will do one for you, and you try the other two
2.
3n + 9/10 + n/5= -2 3/10
3n + 9/10 + n/5= -23/10
looks like 10 is the lowest common denominator, so multiply each term by 10
30n + 9 + 2n = -23
32n = - 23 - 9
32n = - 32
n = -1
hint: for the first, multiply each term by 24
for the third, multiply each term by 12
i got for # 3 8/13 and plugged in the number for the letters and got it wrong. what is the correct way to solve it thank you
#3
3k/4 - 28 - 2k/3 = 37
times 12
9k - 336 - 8k = 444
k = 444+336
k = 780
check:
Left side = 3(780)/4 - 28 - 2(780)/3
= 585 - 28 - 520
= 37
= right side
My answer is correct, how did you get 8/13 ?
Sure! I'll be happy to help you solve these problems step by step. Let's start with problem 1:
1. 2x/3 + 1/3 - x/8 = 2/3.
To solve this equation, we need to get rid of the fractions. To do that, we'll multiply all terms by a common multiple of the denominators, which in this case is 24. By multiplying both sides of the equation by 24, we can get rid of the fractions:
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, we need to isolate the variable x, so we'll subtract 8 from both sides:
13x = 16 - 8,
which simplifies to:
13x = 8.
Finally, to solve for x, we divide both sides by 13:
x = 8/13.
So the solution to the equation is x = 8/13.
Let's move on to problem 2:
2. 3n + 9/10 + n/5 = -2 3/10.
Similar to problem 1, we'll eliminate the fractions by multiplying all terms by a common multiple of the denominators, which in this case is 10. By multiplying both sides of the equation by 10, we can clear the fractions:
10 * (3n) + 10 * (9/10) + 10 * (n/5) = 10 * (-2 3/10).
This simplifies to:
30n + 9 + 2n = -23.
Combining like terms, we have:
32n + 9 = -23.
Next, let's isolate the variable n by subtracting 9 from both sides:
32n = -23 - 9,
which simplifies to:
32n = -32.
To solve for n, we divide both sides by 32:
n = -32/32.
Simplifying further:
n = -1.
Therefore, the solution to the equation is n = -1.
Finally, let's solve problem 3:
3. 3k/4 - 28 - 2k/3 = 37.
Similar to the previous problems, we'll eliminate the fractions by finding a common multiple of the denominators, which in this case is 12. By multiplying both sides by 12, we clear the fractions:
12 * (3k/4) - 12 * 28 - 12 * (2k/3) = 12 * 37.
This simplifies to:
9k - 336 - 8k = 444.
Combining like terms, we have:
k - 336 = 444.
To isolate the variable k, we'll add 336 to both sides:
k = 444 + 336,
which simplifies to:
k = 780.
Therefore, the solution to the equation is k = 780.
I hope this helps! Let me know if you have any further questions.