Graph the inequality on the numberline and then write it in interval notation.
2/3a-1/4a<5/12a-3/4
2/3a-1/4a<5/12a-3/4
I would multiply each term by 12, the LCD
8a - 3 < 5a - 9
I am sure you can do it from here
To graph the inequality on a number line and write it in interval notation, we need to solve the inequality first. Here are the steps to do that:
Step 1: Combine like terms on each side of the inequality.
2/3a - 1/4a < 5/12a - 3/4
To combine the fractions, we need to find a common denominator. The least common multiple (LCM) of 3, 4, and 12 is 12.
Multiplying each term by 12 to clear the fractions, we get:
8(2a) - 3(1a) < 5(1a) - 9(3)
Simplifying further, we have:
16a - 3a < 5a - 27
Step 2: Solve the inequality for 'a'.
13a < 5a - 27
To isolate the variable 'a', we can subtract 5a from both sides:
13a - 5a < 5a - 5a - 27
8a < -27
To solve for 'a', divide both sides by 8 (note that we divide by a positive number, so the inequality sign does not change):
a < -27/8
Step 3: Graph the inequality on the number line.
Since the inequality is a "less than" symbol (a < -27/8), the number -27/8 is not included in the solution. So we should graph an open circle at -27/8 on the number line. Then, draw an arrow to the left, indicating that all values less than -27/8 are solutions.
***--->
-4 -3 -2 -1 0 1 2 3 4
In this case, the arrow should point to the left starting from -27/8.
Step 4: Write the inequality in interval notation.
Since the inequality is a "less than" sign, the interval notation will be (-∞, -27/8). The symbol (-∞) represents all real numbers less than -27/8.
Therefore, the inequality 2/3a - 1/4a < 5/12a - 3/4 is graphed as an open circle at -27/8 on the number line, with an arrow pointing to the left, and it is written in interval notation as (-∞, -27/8).