I need help with 4 mat problems. I do not know how to set up to solve.
x/8=-6
-4/9+(-5/7)
x-4/5=6/7
7/x=?/xsquared
1.Multiply both sides of the first equation by 8
2. convert each fraction to have a (common) denomiator of 63. Then add the numerators
3. Multiply both sides of the equation by 35 and yet 7(x-4) = 30
Then solve that.
4. I assume you mean (7/x) = y/x^2
where y is a new unknown that you indicate by ?
xy = 7x^2
y = 7x
Sure! I can help you with these math problems. Let's go through each problem step by step and explain how to set up and solve them.
1. x/8 = -6:
To solve this equation, we can multiply both sides by 8 to isolate the variable x. Multiplying both sides by 8 cancels out the denominator, giving us:
8 * (x/8) = 8 * (-6)
x = -48
2. -4/9 + (-5/7):
To add or subtract fractions, we need to have a common denominator. In this case, we can find the least common multiple (LCM) of 9 and 7, which is 63. Now, we can rewrite the fractions with a common denominator:
(-4/9) * (7/7) + (-5/7) * (9/9)
(-28/63) + (-45/63)
Now that the fractions have a common denominator, we can combine the numerators while keeping the denominator the same:
(-28 - 45) / 63
-73/63
3. x - 4/5 = 6/7:
To solve this equation, we want to isolate the variable x. Firstly, let's get rid of the fraction by multiplying both sides by 5:
5 * (x - 4/5) = 5 * (6/7)
5x - 4 = (30/7)
Next, we want to get rid of the constant term (-4) by adding 4 to both sides:
5x - 4 + 4 = (30/7) + 4
5x = (30/7) + (28/7)
5x = (58/7)
Finally, to get x by itself, we divide both sides by 5:
5x/5 = (58/7) / 5
x = (58/7) * (1/5)
x = 58/35
4. 7/x = ?/x^2:
To solve this equation, we can cross-multiply. Cross-multiplication involves multiplying the numerator of the first fraction with the denominator of the second fraction, and vice versa. Let's set up the equation:
7/x = ?/x^2
Now, we can cross-multiply:
7 * x^2 = ? * x
7x^2 = ?x
At this point, we can see that the variable ? is missing, and there is not enough information to determine its value. So, we can't find the exact value of ? in this case.