x-5<x/6
To solve the inequality, we can multiply both sides of the inequality by 6 to eliminate the fraction. This gives us:
6(x-5) < x.
Expanding the expression on the left side, we get:
6x - 30 < x.
Now, we can subtract 6x from both sides of the inequality to isolate the x term:
-30 < x - 6x.
This simplifies to:
-30 < -5x.
To solve for x, we divide both sides of the inequality by -5. However, when dividing by a negative number, we need to flip the direction of the inequality:
30 > 5x.
Finally, divide both sides of the inequality by 5 to solve for x:
6 > x.
Thus, the solution to the inequality is x > 6.
To solve x-5 < x/6 inequality, we can start by simplifying the expression.
Step 1: Multiply through the inequality by 6 to eliminate the fraction:
6 * (x - 5) < x
Step 2: Distribute 6 to both terms inside the parentheses:
6x - 30 < x
Step 3: Move x term to the left side of the inequality:
6x - x < 30
Simplifying the equation further:
5x < 30
Step 4: Divide both sides of the inequality by 5 to solve for x:
(5x)/5 < 30/5
x < 6
Therefore, the solution to the inequality x - 5 < x/6 is x < 6.
To solve the inequality x - 5 < x/6, we need to isolate x on one side of the inequality sign.
Let's start by subtracting x/6 from both sides of the inequality:
x - 5 - x/6 < 0
To combine the terms on the left side, we can find a common denominator for x and 5. The common denominator is 6, so we can rewrite the equation:
6x/6 - 5/1 - x/6 < 0
Simplifying further, we have:
(6x - 5 - x)/6 < 0
Combining like terms, we get:
(5x - 5)/6 < 0
Now, let's multiply both sides of the inequality by 6 to eliminate the denominator:
6 * (5x - 5)/6 < 0 * 6
Simplifying further, we get:
5x - 5 < 0
Next, let's add 5 to both sides of the inequality:
5x - 5 + 5 < 0 + 5
Simplifying further, we have:
5x < 5
To solve for x, divide both sides of the inequality by 5:
(5x)/5 < 5/5
Simplifying further, we get:
x < 1
Therefore, the solution to the inequality x - 5 < x/6 is x < 1.