Answer:
1. Let's start by simplifying the expression on both sides of the inequality. We can begin by finding a common denominator for the fractions involved. The common denominator between 6 and 4 is 12.
x + (3/6) > x/4 + 1
Simplifying the fractions:
x + (1/2) > x/4 + 1
2. Next, let's clear the fractions by multiplying every term in the inequality by 12, the common denominator. This step will eliminate the fractions.
12(x + 1/2) > 12(x/4 + 1)
Distributing and simplifying:
12x + 6 > 3x + 12
3. Now, let's isolate the variable x on one side of the inequality. To do this, we can subtract 3x from both sides:
12x - 3x + 6 > 3x - 3x + 12
Simplifying:
9x + 6 > 12
4. Next, let's isolate the variable x further by subtracting 6 from both sides:
9x + 6 - 6 > 12 - 6
Simplifying:
9x > 6
5. Finally, let's solve for x by dividing both sides of the inequality by 9:
(9x)/9 > 6/9
Simplifying:
x > 2/3
Therefore, the solution to the inequality x + 3/6 > x/4 + 1 is x > 2/3. This means that any value of x greater than 2/3 will make the inequality true.
Explanation: