3/7w+1>9/7-4/5w
To solve the inequality, we need to isolate the variable 'w' on one side.
Let's start by getting rid of fractions by finding a common denominator. The common denominator of 7w and 5w is 35w.
Multiplying every term by 35w, we get:
3(35w/7) + 35w/5 > 9(35w/7) - 4(7w/5)
This simplifies to:
15w + 7(7w/5) > 45w - 28w/5
15w + 49w/5 > 45w - 28w/5
Now, let's combine like terms:
(75w + 49w) / 5 > (225w - 28w) / 5
(124w) / 5 > (197w) / 5
Now, we can cancel out the denominators:
124w > 197w
Next, we want to isolate the variable 'w' on one side. Subtracting 197w from both sides, we get:
124w - 197w > 0
-73w > 0
Finally, we divide both sides by -73, remembering to flip the inequality sign:
w < 0/-73
w < 0
Therefore, the solution to the inequality is w < 0.
To solve the inequality:
3/7w + 1 > 9/7 - 4/5w
Step 1: Start by getting rid of the fractions by finding the common denominator. In this case, the common denominator is 35.
Multiply every term by 35 to clear the fractions:
35(3/7w + 1) > 35(9/7 - 4/5w)
Step 2: Distribute the multiplication on both sides:
(35 * 3/7)w + 35(1) > (35 * 9/7) - (35 * 4/5w)
Step 3: Simplify each term:
(15/7)w + 35 > 45/7 - (28/5)w
Step 4: Combine like terms on both sides.
To do this, convert all terms to the same denominator, which is 35.
Multiply (15/7)w by 5/5 to get (75/35)w.
Multiply (28/5)w by 7/7 to get (196/35)w.
(75/35)w + 35 > 45/7 - (196/35)w
Step 5: Combine like terms:
(75/35 - 196/35)w + 35 > 45/7
Simplify:
(-121/35)w + 35 > 45/7
Step 6: Bring like terms with 'w' to one side and numbers to the other side.
To do this, subtract 35 from both sides:
(-121/35)w + 35 - 35 > 45/7 - 35
Simplify:
(-121/35)w > 45/7 - (5*7/7)
(-121/35)w > 45/7 - 35/7
(-121/35)w > (45 - 35)/7
(-121/35)w > 10/7
Step 7: Divide both sides by (-121/35). Remember to reverse the inequality sign when dividing by a negative number.
w < (10/7) / (-121/35)
Simplify by multiplying by the reciprocal:
w < (10/7) * (-35/121)
w < -350/847
So the solution to the inequality is w < -350/847.
To solve the inequality 3/7w + 1 > 9/7 - 4/5w, we can use the following steps:
Step 1: Simplify the expressions on both sides of the inequality.
On the left side, we have 3/7w + 1. The right side consists of 9/7 - 4/5w.
Step 2: Let's start by getting rid of the fractions by multiplying every term by the least common denominator (LCD) of the denominators, which is 35 in this case.
For the left side:
Multiply 1 by 35/35: (3/7w) + (1 * 35/35) = (3/7w) + 35/35 = (3/7w) + 35/35
For the right side:
Multiply 9/7 by 35/35: (9/7 * 35/35) - (4/5w * 35/35) = (9 * 35)/(7 * 35) - (4 * 35)/(5 * 35)w = 315/245 -140/175w = 315/245 - (140/175w)
Step 3: Simplify the expressions:
On the left side, there is no further simplification possible.
On the right side, we can simplify:
315/245 - (140/175w) = 315/245 - (4/5w)
Step 4: Rewrite the inequality with the simplified expressions:
The inequality becomes: (3/7w) + (35/35) > (315/245) - (4/5w)
Step 5: Continue simplifying the inequality:
The left side becomes: (3/7w) + (35/35) = (3/7w) + 1
The right side becomes: (315/245) - (4/5w) = (315/245) - (4/5w)
So, the inequality simplifies to: (3/7w) + 1 > (315/245) - (4/5w)
Step 6: Now, we can solve the inequality. Move the terms involving w to one side of the inequality and the constant terms to the other side:
(3/7w) + (4/5w) > (315/245) - 1
Multiply all the terms by the LCD of 35 to eliminate the fractions:
(35 * (3/7w)) + (35 * (4/5w)) > (35 * (315/245)) - (35 * 1)
(15w) + (28w) > (45 * 3) - 35
Step 7: Simplify the expressions:
43w > 135 - 35
43w > 100
Step 8: Solve for w by isolating the variable w:
Divide both sides of the inequality by 43:
w > 100/43
So the solution to the given inequality is w > 100/43.