Find the solution to the inequality 4y + 2 < 50.

9 answers

Subtract 2 from both sides:

4y < 48

Divide both sides by 4:

y < 12

Therefore, the solution to the inequality is y < 12.
What would the solution y<3 look like if you were to represent it graphically?
To represent the inequality y < 3 graphically, you would draw a dashed horizontal line at y = 3 on the y-axis. Then shade the region below the line, indicating all values of y that are less than 3. This shaded region would extend downwards from the dashed line to negative infinity.

In other words, your graph would show all y-values less than 3, but not including 3 itself.
Is it a open or close circle?
Since the inequality is y < 3 (not y ≤ 3), the circle at y = 3 should be an open circle. This indicates that the value of y cannot equal 3, only values less than 3 are included in the solution set.
Left or right?
In this case, since the inequality is y < 3, the shaded region would be to the left of the y = 3 line. This means that the values of y that satisfy the inequality are to the left of 3 on the number line.
Find the solution to the inequality x/7 + 13 > 20.
Subtract 13 from both sides:

x/7 > 7

Multiply both sides by 7:

x > 49

Therefore, the solution to the inequality is x > 49.