Question

section 2.1 classwork
write each sentence as an inequality
1 a number x is greater than 3.
2 a number n plus 7 is less than or equal to 9.
3 25 is at most 4 times a number y minus 8.
4 graph the inequality
a ( x geq 4 )
b ( -3 > j )
determine whether the given is a solution of the inequality
5 ( r + 4 > 8 ); ( r = 2 )
6.

value of ( x )	( 3x leq 24 )	is the inequality true?
( 8 )

solve for the indicated variable.
7 ( d = rt ); solve for ( r )
8 solve for ( y ).
( 4x - 7y = 12 )
solve the equation
9 ( -4(2x + 6) - 12 = 4 )
10 ( 3(n + 4) = \frac{1}{2}(6n + 4) )

Explanation:

Step1: Translate sentence to inequality

$x > 3$

Step2: Translate sentence to inequality

$n + 7 \leq 9$

Step3: Translate sentence to inequality

$25 \leq 4y - 8$

Step4a: Graph $x\geq4$

• Plot a closed circle at $x=4$ on the number line, shade all values to the right of 4 (including 4).

Step4b: Graph $-3 > j$

• Plot an open circle at $j=-3$ on the number line, shade all values to the left of -3 (excluding -3).

Step5: Test $r=2$ in inequality

Substitute $r=2$ into $r+4>8$:
$2 + 4 = 6$; $6 > 8$ is false.

Step6: Evaluate $3x\leq24$ for given $x$

For $x=-4$:

$3(-4) = -12$; $-12 \leq 24$ is true.

For $x=8$:

$3(8) = 24$; $24 \leq 24$ is true.

Step7: Solve $d=vt$ for $v$

Divide both sides by $t$:
$v = \frac{d}{t}$

Step8: Solve $4x-7y=12$ for $y$

Subtract $4x$: $-7y = 12 - 4x$
Divide by $-7$: $y = \frac{4x - 12}{7}$

Step9: Solve $-4(2x+6)-12=4$

Expand: $-8x -24 -12 = 4$
Simplify: $-8x -36 = 4$
Add 36: $-8x = 40$
Divide by $-8$: $x = -5$

Step10: Solve $3(n+4)=\frac{1}{2}(6n+4)$

Expand: $3n + 12 = 3n + 2$
Subtract $3n$: $12 = 2$, which is false (no solution).

Answer:

1. $x > 3$
2. $n + 7 \leq 9$
3. $25 \leq 4y - 8$

4a. Closed circle at 4, shade right
4b. Open circle at -3, shade left

1. No, $r=2$ is not a solution

6.

Value of $x$	$3x \leq 24$	Is the inequality true?
$8$	$24 \leq 24$	Yes

1. $v = \frac{d}{t}$
2. $y = \frac{4x - 12}{7}$
3. $x = -5$
4. No solution