Question

inequalities with tables
think about the inequality, $x - 3 > -2$.
which values of $x$ in the table make this inequality true?
(select all that apply.)
$\square$ $-4$
$\square$ $-3$
$\square$ $-2$
$\square$ $-1$
$\square$ $0$
$\square$ $1$
$\square$ $2$
$\square$ $3$
$\square$ $4$
table with columns x and x - 3 and rows for x = -4, -3, -2, -1, 0, 1, 2, 3, 4 with corresponding x - 3 values: -7, -6, -5, -4, -3, -2, -1, 0, 1

Explanation:

Step1: Solve the inequality \( x - 3 > -2 \)

Add 3 to both sides of the inequality: \( x - 3 + 3 > -2 + 3 \), which simplifies to \( x > 1 \).

Step2: Check each value of \( x \) in the table against \( x > 1 \)

• For \( x = -4 \): \( -4 > 1 \)? No.
• For \( x = -3 \): \( -3 > 1 \)? No.
• For \( x = -2 \): \( -2 > 1 \)? No.
• For \( x = -1 \): \( -1 > 1 \)? No.
• For \( x = 0 \): \( 0 > 1 \)? No.
• For \( x = 1 \): \( 1 > 1 \)? No (since it's equal, not greater).
• For \( x = 2 \): \( 2 > 1 \)? Yes.
• For \( x = 3 \): \( 3 > 1 \)? Yes.
• For \( x = 4 \): \( 4 > 1 \)? Yes.

Answer:

2, 3, 4 (corresponding to the options:
\(\square\) 2
\(\square\) 3
\(\square\) 4)