Question

inequalities with tables
lets investigate the inequality $x - 3 > -2$.
complete the table.

$x$	$x - 3$
$-3$
$-2$	$-5$
$-1$
$0$
$1$
$2$	$-1$
$3$
$4$	$1$

check my work!

Explanation:

Step1: For \( x = -3 \), calculate \( x - 3 \)

Substitute \( x = -3 \) into \( x - 3 \), we get \( -3 - 3 = -6 \)

Step2: For \( x = -1 \), calculate \( x - 3 \)

Substitute \( x = -1 \) into \( x - 3 \), we get \( -1 - 3 = -4 \)

Step3: For \( x = 0 \), calculate \( x - 3 \)

Substitute \( x = 0 \) into \( x - 3 \), we get \( 0 - 3 = -3 \)

Step4: For \( x = 1 \), calculate \( x - 3 \)

Substitute \( x = 1 \) into \( x - 3 \), we get \( 1 - 3 = -2 \)

Step5: For \( x = 3 \), calculate \( x - 3 \)

Substitute \( x = 3 \) into \( x - 3 \), we get \( 3 - 3 = 0 \)

Filled Table:

\( x \)	\( x - 3 \)
-3	-6
-2	-5
-1	-4
0	-3
1	-2
2	-1
3	0
4	1

(If you just need the calculated values for each blank: for \( x=-3 \), \( x - 3=-6 \); for \( x = -1 \), \( x - 3=-4 \); for \( x = 0 \), \( x - 3=-3 \); for \( x = 1 \), \( x - 3=-2 \); for \( x = 3 \), \( x - 3=0 \))

Answer:

Step1: For \( x = -3 \), calculate \( x - 3 \)

Substitute \( x = -3 \) into \( x - 3 \), we get \( -3 - 3 = -6 \)

Step2: For \( x = -1 \), calculate \( x - 3 \)

Substitute \( x = -1 \) into \( x - 3 \), we get \( -1 - 3 = -4 \)

Step3: For \( x = 0 \), calculate \( x - 3 \)

Substitute \( x = 0 \) into \( x - 3 \), we get \( 0 - 3 = -3 \)

Step4: For \( x = 1 \), calculate \( x - 3 \)

Substitute \( x = 1 \) into \( x - 3 \), we get \( 1 - 3 = -2 \)

Step5: For \( x = 3 \), calculate \( x - 3 \)

Substitute \( x = 3 \) into \( x - 3 \), we get \( 3 - 3 = 0 \)

Filled Table:

\( x \)	\( x - 3 \)
-3	-6
-2	-5
-1	-4
0	-3
1	-2
2	-1
3	0
4	1

(If you just need the calculated values for each blank: for \( x=-3 \), \( x - 3=-6 \); for \( x = -1 \), \( x - 3=-4 \); for \( x = 0 \), \( x - 3=-3 \); for \( x = 1 \), \( x - 3=-2 \); for \( x = 3 \), \( x - 3=0 \))