Question

2 exploration: writing a rule work with a partner. a. complete the table. decide which graph represents the solution of the inequality 6 < -3x. write the solution of the inequality. x | -5 | -4 | -3 | -2 | -1 | 0 | 1 -3x | | | | | | | 6 < -3x | | | | | | |

Explanation:

Step1: Calculate -3x for each x

For \( x = -5 \): \(-3\times(-5)=15\)
For \( x = -4 \): \(-3\times(-4)=12\)
For \( x = -3 \): \(-3\times(-3)=9\)
For \( x = -2 \): \(-3\times(-2)=6\)
For \( x = -1 \): \(-3\times(-1)=3\)
For \( x = 0 \): \(-3\times0 = 0\)
For \( x = 1 \): \(-3\times1=-3\)

Step2: Check \( 6 < -3x \) for each x

For \( x = -5 \): \( 6 < 15 \) → True
For \( x = -4 \): \( 6 < 12 \) → True
For \( x = -3 \): \( 6 < 9 \) → True
For \( x = -2 \): \( 6 < 6 \) → False
For \( x = -1 \): \( 6 < 3 \) → False
For \( x = 0 \): \( 6 < 0 \) → False
For \( x = 1 \): \( 6 < -3 \) → False

Step3: Solve the inequality \( 6 < -3x \)

Divide both sides by -3 (remember to reverse inequality sign):
\( \frac{6}{-3} > x \) → \( -2 > x \) or \( x < -2 \)

Answer:

Table Completion:

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

Solution of Inequality: \( x < -2 \)