1. x+1/2=7
2. 1/3x-5/3=8/3
3. 4/7x=-20
4. 3/4x+11=23
5. 4/5x+7/3=14/
6. -(10-x)=(x+4)
ive always been bad at these kinds of problems w/ the fractions, any help would be appreciated!!! :o)
question 5 should have been 4/5x+7/3=14/5 !!! sorry!!!
If you know how to find the lowest common denominator for fractions,
then you know how to do these questions.
Look at #5
4/5x+7/3=14/5
the denominators are 5 and 3, so the LCD is 15
now simply multiply each term by 15
15(4/5)x + 15(7/3) = 15(14/5)
12x + 35 = 42
See how easy it becomes now?
I don't know why you included #6 -(10-x)=(x+4) ?
-10 + x = x + 4
ahh, I see why, the x drops out, so you get
-10 = 4 which of course is nonsense.
if you get "nonsense" as a result after the variable drops out,
there is no solution to your equation.
if you get a true statement as a result after the variable drops out,
there will be an infinite number of solutions.
Sure! I'll help you solve each of these equations step by step. Don't worry, we'll take it one problem at a time.
1. x + 1/2 = 7
To solve for x, we want to isolate it on one side of the equation. Start by subtracting 1/2 from both sides:
x + 1/2 - 1/2 = 7 - 1/2
x = 6 1/2 or 6.5
2. 1/3x - 5/3 = 8/3
To deal with fractions, we can first clear the denominators by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. In this case, the LCM is 3. Multiply each term by 3:
3 * (1/3x) - 3 * (5/3) = 3 * (8/3)
x - 5 = 8
Next, add 5 to both sides to isolate x:
x - 5 + 5 = 8 + 5
x = 13
3. 4/7x = -20
To solve for x, we want to get rid of the fraction. Multiply both sides of the equation by the reciprocal of 4/7, which is 7/4:
(7/4) * (4/7)x = (7/4) * (-20)
(7/7)x = -140/4
x = -35
4. 3/4x + 11 = 23
To start, subtract 11 from both sides:
3/4x + 11 - 11 = 23 - 11
3/4x = 12
To eliminate the fraction, multiply both sides by the reciprocal of 3/4, which is 4/3:
(4/3) * (3/4)x = (4/3) * (12)
x = 16
5. 4/5x + 7/3 = 14
To eliminate the fractions, we need to find a common denominator. In this case, the least common denominator is 15. Multiply each term by 15:
15 * (4/5x) + 15 * (7/3) = 15 * 14
12x + 35 = 210
Next, subtract 35 from both sides:
12x + 35 - 35 = 210 - 35
12x = 175
Finally, divide both sides by 12 to solve for x:
x = 14 5/12 or 14.4167 (approx.)
6. -(10 - x) = (x + 4)
To solve this equation, we'll distribute the negative sign to the terms inside the parentheses:
-10 + x = x + 4
Next, we want to isolate the x terms on one side and the constant terms on the other. In this case, subtract x from both sides:
-10 + x - x = x - x + 4
-10 = 4
Since there is no value of x that satisfies the equation, this equation does not have a solution.
I hope this explanation helps you understand how to solve equations with fractions. If you have any further questions, feel free to ask!