Graph the inequality on the numberline and then write it in interval notation.
5/3y < 10
multiplying by 3/5
y < 6
an open circle at 6
arrow going to the left
To graph the inequality on the number line, we need to first solve it for y.
5/3y < 10
To isolate y, we can multiply both sides of the inequality by 3/5 (the reciprocal of 5/3).
(3/5)(5/3)y < (3/5)(10)
1y < 6
y < 6
Now we can graph the inequality on the number line. We represent the solution as an open circle at 6 and shade everything to the left of 6.
```
------------------------o-------->
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
```
To write the inequality in interval notation, we use parentheses to indicate that the endpoint is not included:
(-∞, 6)
To graph the inequality 5/3y < 10 on a number line, we need to solve it first. Here's how to do it step by step:
Step 1: Begin by isolating y by dividing both sides of the inequality by 5/3.
(5/3y) / (5/3) < 10 / (5/3)
Simplifying, we get:
y < (10 / (5/3))
Step 2: To simplify further, divide 10 by 5/3. Remember that dividing by a fraction is the same as multiplying by its reciprocal.
y < (10 * (3/5))
Simplifying the multiplication:
y < (30/5)
y < 6
So, the solution to the inequality is y < 6.
Now, let's represent this on a number line:
First, draw a number line with 0 in the center.
Next, mark a filled circle at 6 (since y is less than 6).
Finally, draw an arrow pointing to the left starting from the filled circle, indicating that all values of y less than 6 satisfy the inequality.
The graph will look like this:
-∞ →==================●--------------------→ ∞
6
In interval notation, we write the solution as (-∞, 6), which means all real numbers less than 6, including negative infinity.