Solve the following inequality for ww. Write your answer in simplest form.
10, w, minus, 9, is greater than, 6, w, plus, 9
10w−9>
6w+9
To solve the inequality, we need to isolate the variable w on one side of the equation.
Starting with the given inequality:
10w - 9 > 6w + 9
We can subtract 6w from both sides to get rid of the term with w on the right side:
10w - 6w - 9 > 9
Simplifying this gives:
4w - 9 > 9
Next, we can add 9 to both sides:
4w - 9 + 9 > 9 + 9
Simplifying further gives:
4w > 18
Finally, we can divide both sides of the inequality by 4 to solve for w:
w > 18/4
Simplifying the expression gives:
w > 9/2
So the solution to the inequality is w > 9/2.
To solve the inequality 10w - 9 > 6w + 9, we will follow these steps:
Step 1: Combine like terms on both sides of the inequality.
Starting with the left side, we have 10w - 9. There are no like terms to combine.
Moving to the right side, we have 6w + 9. Again, there are no like terms to combine.
Our inequality remains as 10w - 9 > 6w + 9.
Step 2: Move all terms containing the variable w to one side and the constant terms to the other side.
To do this, we will subtract 6w from both sides and add 9 to both sides.
(10w - 9) - 6w > (6w + 9) - 6w + 9
Simplifying this expression, we get:
4w - 9 > 9
Step 3: Simplify further, if necessary.
To isolate the variable w, we will add 9 to both sides of the inequality.
(4w - 9) + 9 > 9 + 9
Simplifying this expression, we get:
4w > 18
Step 4: Divide both sides of the inequality by the coefficient of w, which is 4.
(4w)/4 > 18/4
Simplifying this expression, we get:
w > 4.5
So the solution to the inequality 10w - 9 > 6w + 9 is w > 4.5.
To solve the inequality, we need to isolate the variable "w" on one side of the inequality symbol.
Step 1: Start by subtracting 6w from both sides of the inequality:
10w - 9 - 6w > 9
Simplifying the left side of the inequality:
(10w - 6w) - 9 > 9
4w - 9 > 9
Step 2: Next, add 9 to both sides of the inequality:
4w - 9 + 9 > 9 + 9
Simplifying:
4w > 18
Step 3: To isolate "w," divide both sides of the inequality by 4:
(4w) / 4 > 18 / 4
Simplifying:
w > 4.5
Therefore, the solution to the inequality is w > 4.5.