Question

what does the solution to ( x + 4 > 6 ) look like on a number line?
a. open circle at 2, shading to the right
b. closed circle at 2, shading to the right
c. open circle at 2, shading to the left
d. closed circle at 2, shading to the left

if ( 3x - 7 > 11 ), what is the solution for ( x )?
a. ( x > 6 )
b. ( x < \frac{18}{3} )
c. ( x leq \frac{18}{3} )
d. ( x > \frac{18}{3} )

Explanation:

Step1: Solve first inequality

$x + 4 > 6 \implies x > 2$

Step2: Represent on number line

Open circle at 2 (no equality), shade right (values >2)

Step3: Solve second inequality

$3x - 7 > 11 \implies 3x > 18 \implies x > \frac{18}{3}$

Answer:

a. Open circle at 2, shading to the right
d. $x > \frac{18}{3}$