Question

translate each statement into symbols.

1. the number n is less than 20.
2. the absolute value of - 2 is greater than 1.
3. 6x - 3 < 7 + 4x and graph solution set.
4. - 8 is between 0 and - 10.
5. 5 is between - 9 and 9.
6. 4.6 is greater than 4 and 4 is greater than 0.
7. - 1.5 is less than - 1 and - 1 is less than 0.

Explanation:

Step1: Translate "The number n is less than 20"

$n < 20$

Step2: Translate " - 8 is between 0 and - 10"

$ - 10 < - 8 < 0$

Step3: Translate "5 is between - 9 and 9"

$ - 9 < 5 < 9$

Step4: Translate "The absolute value of - 2 is greater than 1"

$|-2|>1$

Step5: Translate "46 is greater than 4 and 4 is greater than 0"

$46 > 4>0$

Step6: Translate " - 15 is less than - 1 and - 1 is less than 0"

$ - 15 < - 1 < 0$

Step7: Solve the inequality $6x - 3<7 + 4x$

First, subtract $4x$ from both sides:
$6x-4x - 3<7+4x-4x$
$2x - 3<7$
Then, add 3 to both sides:
$2x-3 + 3<7 + 3$
$2x<10$
Divide both sides by 2:
$x < 5$
To graph the solution set on a number - line, draw an open circle at 5 (since $x$ is less than 5, not less than or equal to 5) and shade the line to the left of 5.

Answer:

1. $n < 20$
2. $ - 10 < - 8 < 0$
3. $ - 9 < 5 < 9$
4. $|-2|>1$
5. $46 > 4>0$
6. $ - 15 < - 1 < 0$
7. Solution of $6x - 3<7 + 4x$ is $x < 5$, graph: open - circle at 5, shade to the left.