Question

solve for ( x ) and graph the solution on the number line below. if possible, resolve your answer to a single inequality. in case of no solution (( varnothing )), leave the number line blank.

( -33 < 5x - 3 ) or ( 37 leq 5x - 3 )

answer

inequality notation: (\boxed{quad})

number line:

(\boxed{quad})

Explanation:

Step1: Solve left inequality, add 3

$-33 + 3 < 5x - 3 + 3$
$-30 < 5x$

Step2: Isolate x, divide by 5

$\frac{-30}{5} < \frac{5x}{5}$
$-6 < x$

Step3: Solve right inequality, add 3

$37 + 3 \leq 5x - 3 + 3$
$40 \leq 5x$

Step4: Isolate x, divide by 5

$\frac{40}{5} \leq \frac{5x}{5}$
$8 \leq x$

Step5: Combine solutions with "or"

$x > -6$ or $x \geq 8$ simplifies to $x > -6$ (since $x \geq 8$ is a subset of $x > -6$)

Answer:

Inequality Notation:

$x > -6$

Number Line:

Draw an open circle at $-6$ on the number line, then shade all regions to the right of $-6$ (extending to positive infinity).