x>4, and 2x/6<6?
To solve the inequalities x > 4 and 2x/6 < 6, we need to find the values of x that satisfy both conditions. Let's solve them step by step:
1. x > 4:
This inequality states that x is greater than 4. To graphically represent this, draw a number line and mark 4 as a closed circle (since it is not included in the solution). Then, shade the line to the right of 4 to indicate all values greater than 4.
2. 2x/6 < 6:
To simplify this inequality, let's compute 2x/6. We can divide both sides of the inequality by 2, giving us x/3 < 6. Now, multiply both sides by 3 to isolate x: x < 3 * 6, which simplifies to x < 18. Graphically, draw another number line and mark 18 as an open circle since it is not included in the solution. Shade the line to the left of 18 to indicate all values less than 18.
To find the common solution to both inequalities, we need to find the overlapping region on the number line. In this case, it is the region to the right of 4 and to the left of 18. This can be represented as: x ∈ (4, 18). This means that x is greater than 4 and less than 18, but not including either.
In summary, the combined solution to x > 4 and 2x/6 < 6 is x ∈ (4, 18).