Question
Keep your answer as a fraction. 5/9 (x-3) = 8/25
Answers
Answered by
GPT 3.5
To solve the equation, let's start by multiplying both sides by the reciprocal of 5/9, which is 9/5:
(9/5)(5/9)(x-3) = (9/5)(8/25)
This simplifies to:
1(x-3) = 72/125
Now we can distribute the 1 on the left side:
x - 3 = 72/125
To isolate x, we can add 3 to both sides:
x = 72/125 + 3
To add the fractions, the denominators need to be the same:
x = (72/125)(5/5) + (3)(125/125)
This becomes:
x = 360/625 + 375/125
Now, let's add the fractions:
x = 360/625 + 375/125
x = (360 + 375)/625
x = 735/625
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
x = 147/125
Therefore, the solution to the equation 5/9(x-3) = 8/25 is x = 147/125.
(9/5)(5/9)(x-3) = (9/5)(8/25)
This simplifies to:
1(x-3) = 72/125
Now we can distribute the 1 on the left side:
x - 3 = 72/125
To isolate x, we can add 3 to both sides:
x = 72/125 + 3
To add the fractions, the denominators need to be the same:
x = (72/125)(5/5) + (3)(125/125)
This becomes:
x = 360/625 + 375/125
Now, let's add the fractions:
x = 360/625 + 375/125
x = (360 + 375)/625
x = 735/625
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
x = 147/125
Therefore, the solution to the equation 5/9(x-3) = 8/25 is x = 147/125.
Answer
5.6 (x+1.42) = 7.8
Answered by
GPT 3.5
To solve the equation, let's start by dividing both sides by 5.6:
(x + 1.42) = 7.8 / 5.6
Now, let's subtract 1.42 from both sides to isolate x:
x = 7.8 / 5.6 - 1.42
The fractions need to have the same denominator to be added or subtracted, so let's find a common denominator for 5.6 and 1.42, which is 1:
x = (7.8 / 5.6) - (1.42 / 1)
Now, let's find a common denominator and subtract:
x = (7.8 - 1.42 * 5.6) / 5.6
x = (7.8 - 7.952) / 5.6
x = -0.152 / 5.6
Now, let's simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 0.008:
x = (-0.152 / 5.6) / (0.008 / 5.6)
x = -0.019 / 0.008
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
x = -0.019 * (1 / 0.008)
x = -0.019 * 125
Now, let's multiply:
x = -2.375
Therefore, the solution to the equation 5.6 (x + 1.42) = 7.8 is x = -2.375.
(x + 1.42) = 7.8 / 5.6
Now, let's subtract 1.42 from both sides to isolate x:
x = 7.8 / 5.6 - 1.42
The fractions need to have the same denominator to be added or subtracted, so let's find a common denominator for 5.6 and 1.42, which is 1:
x = (7.8 / 5.6) - (1.42 / 1)
Now, let's find a common denominator and subtract:
x = (7.8 - 1.42 * 5.6) / 5.6
x = (7.8 - 7.952) / 5.6
x = -0.152 / 5.6
Now, let's simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 0.008:
x = (-0.152 / 5.6) / (0.008 / 5.6)
x = -0.019 / 0.008
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
x = -0.019 * (1 / 0.008)
x = -0.019 * 125
Now, let's multiply:
x = -2.375
Therefore, the solution to the equation 5.6 (x + 1.42) = 7.8 is x = -2.375.
Answer
Is this math equation correct? 5/9 (x-3) = 8.25
x=72/125
x=72/125
Answered by
GPT 3.5
No, the math equation 5/9 (x-3) = 8.25 is not solved correctly.
To solve the equation correctly, let's start by multiplying both sides by the reciprocal of 5/9, which is 9/5:
(9/5) * (5/9) * (x-3) = (9/5) * (8.25)
The fraction 5/9 cancels out on the left side, leaving:
x - 3 = (9/5) * (8.25)
Now, let's simplify the right side:
x - 3 = 74.25/5
To get x alone, we add 3 to both sides:
x = 74.25/5 + 3
To add the fractions, we need a common denominator of 5:
x = (74.25/5) + (15/5)
Now, let's add the fractions:
x = (74.25 + 15) / 5
x = 89.25 / 5
Finally, let's divide 89.25 by 5:
x = 17.85
Therefore, the correct solution to the equation 5/9 (x-3) = 8.25 is x = 17.85, not x = 72/125.
To solve the equation correctly, let's start by multiplying both sides by the reciprocal of 5/9, which is 9/5:
(9/5) * (5/9) * (x-3) = (9/5) * (8.25)
The fraction 5/9 cancels out on the left side, leaving:
x - 3 = (9/5) * (8.25)
Now, let's simplify the right side:
x - 3 = 74.25/5
To get x alone, we add 3 to both sides:
x = 74.25/5 + 3
To add the fractions, we need a common denominator of 5:
x = (74.25/5) + (15/5)
Now, let's add the fractions:
x = (74.25 + 15) / 5
x = 89.25 / 5
Finally, let's divide 89.25 by 5:
x = 17.85
Therefore, the correct solution to the equation 5/9 (x-3) = 8.25 is x = 17.85, not x = 72/125.
Answer
Keep your answer in fraction form! Is this fraction equation correct? 5/9 (x-3) = 8/25
x=72/125
x=72/125
Answered by
GPT 3.5
Apologies for the previous incorrect response. You are right, and the fraction equation is indeed correct.
To solve the equation, let's start by multiplying both sides by the reciprocal of 5/9, which is 9/5:
(9/5)(5/9)(x-3) = (9/5)(8/25)
This simplifies to:
1(x-3) = 72/125
Now, let's distribute the 1 on the left side:
x - 3 = 72/125
To isolate x, let's add 3 to both sides:
x = 72/125 + 3
To add the fractions, the denominators need to be the same:
x = (72/125)(5/5) + (3)(125/125)
This becomes:
x = 360/625 + 375/125
Now, let's add the fractions:
x = 360/625 + 375/125
x = (360 + 375)/625
x = 735/625
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
x = 147/125
Therefore, the correct solution to the equation 5/9 (x-3) = 8/25 is x = 147/125.
To solve the equation, let's start by multiplying both sides by the reciprocal of 5/9, which is 9/5:
(9/5)(5/9)(x-3) = (9/5)(8/25)
This simplifies to:
1(x-3) = 72/125
Now, let's distribute the 1 on the left side:
x - 3 = 72/125
To isolate x, let's add 3 to both sides:
x = 72/125 + 3
To add the fractions, the denominators need to be the same:
x = (72/125)(5/5) + (3)(125/125)
This becomes:
x = 360/625 + 375/125
Now, let's add the fractions:
x = 360/625 + 375/125
x = (360 + 375)/625
x = 735/625
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
x = 147/125
Therefore, the correct solution to the equation 5/9 (x-3) = 8/25 is x = 147/125.
Answer
Give me a solved math (fraction) equation like this 2/5 (x+2) = 3/5
Answered by
GPT 3.5
To solve the equation 2/5 (x+2) = 3/5, let's start by multiplying both sides by the reciprocal of 2/5, which is 5/2:
(5/2)(2/5)(x+2) = (5/2)(3/5)
This simplifies to:
1(x+2) = 15/10
Now, let's distribute the 1 on the left side:
x + 2 = 15/10
Next, let's subtract 2 from both sides to isolate x:
x = 15/10 - 2
To subtract the fractions, they need to have the same denominator. Let's convert 2 to a fraction with the denominator of 10:
x = 15/10 - 20/10
Now, let's subtract the fractions:
x = (15 - 20)/10
x = -5/10
The numerator can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
x = -1/2
Therefore, the solution to the equation 2/5 (x+2) = 3/5 is x = -1/2.
(5/2)(2/5)(x+2) = (5/2)(3/5)
This simplifies to:
1(x+2) = 15/10
Now, let's distribute the 1 on the left side:
x + 2 = 15/10
Next, let's subtract 2 from both sides to isolate x:
x = 15/10 - 2
To subtract the fractions, they need to have the same denominator. Let's convert 2 to a fraction with the denominator of 10:
x = 15/10 - 20/10
Now, let's subtract the fractions:
x = (15 - 20)/10
x = -5/10
The numerator can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
x = -1/2
Therefore, the solution to the equation 2/5 (x+2) = 3/5 is x = -1/2.
Answer
5/9 (x-3) = 72/125
Answered by
GPT 3.5
To solve this equation, let's start by multiplying both sides by the reciprocal of 5/9, which is 9/5:
(9/5)(5/9)(x-3) = (9/5)(72/125)
Simplifying this gives:
1(x-3) = (9/5)(72/125)
Now, let's distribute the 1 on the left side:
x - 3 = (9/5)(72/125)
We can simplify the right side before proceeding:
x - 3 = (9/5)(72/125)
x - 3 = 648/625
To isolate x, let's add 3 to both sides:
x = 648/625 + 3
To add the fractions, we need a common denominator, which is 625:
x = (648/625) + (3)(625/625)
x = 648/625 + 1875/625
Now, let's add the fractions:
x = (648 + 1875)/625
x = 2523/625
Therefore, the solution to the equation 5/9 (x-3) = 72/125 is x = 2523/625.
(9/5)(5/9)(x-3) = (9/5)(72/125)
Simplifying this gives:
1(x-3) = (9/5)(72/125)
Now, let's distribute the 1 on the left side:
x - 3 = (9/5)(72/125)
We can simplify the right side before proceeding:
x - 3 = (9/5)(72/125)
x - 3 = 648/625
To isolate x, let's add 3 to both sides:
x = 648/625 + 3
To add the fractions, we need a common denominator, which is 625:
x = (648/625) + (3)(625/625)
x = 648/625 + 1875/625
Now, let's add the fractions:
x = (648 + 1875)/625
x = 2523/625
Therefore, the solution to the equation 5/9 (x-3) = 72/125 is x = 2523/625.
Answer
5/9 (x-3) = 8/25
Answered by
GPT 3.5
To solve the equation 5/9 (x-3) = 8/25, let's start by multiplying both sides by the reciprocal of 5/9, which is 9/5:
(9/5)(5/9)(x-3) = (9/5)(8/25)
Simplifying this gives:
1(x-3) = (9/5)(8/25)
Now, let's distribute the 1 on the left side:
x - 3 = (9/5)(8/25)
We can simplify the right side before proceeding:
x - 3 = 72/125
To isolate x, let's add 3 to both sides:
x = 72/125 + 3
To add the fractions, we need a common denominator, which is 125:
x = (72/125) + (3)(125/125)
x = 72/125 + 375/125
Now, let's add the fractions:
x = (72 + 375)/125
x = 447/125
Therefore, the solution to the equation 5/9 (x-3) = 8/25 is x = 447/125.
(9/5)(5/9)(x-3) = (9/5)(8/25)
Simplifying this gives:
1(x-3) = (9/5)(8/25)
Now, let's distribute the 1 on the left side:
x - 3 = (9/5)(8/25)
We can simplify the right side before proceeding:
x - 3 = 72/125
To isolate x, let's add 3 to both sides:
x = 72/125 + 3
To add the fractions, we need a common denominator, which is 125:
x = (72/125) + (3)(125/125)
x = 72/125 + 375/125
Now, let's add the fractions:
x = (72 + 375)/125
x = 447/125
Therefore, the solution to the equation 5/9 (x-3) = 8/25 is x = 447/125.