Question

first, solve each inequality. then, graph the solution on the number line. instructions 3 (1/5)x + 14 < 9 4 -193 ≤ -12x - 82

Explanation:

Step1: Isolate term with $x$ (Ineq3)

$\frac{1}{5}x + 14 - 14 < 9 - 14$
$\frac{1}{5}x < -5$

Step2: Solve for $x$ (Ineq3)

$\frac{1}{5}x \times 5 < -5 \times 5$
$x < -25$

Step3: Isolate term with $x$ (Ineq4)

$-193 + 82 \leq -12x - 82 + 82$
$-111 \leq -12x$

Step4: Solve for $x$ (reverse inequality)

$\frac{-111}{-12} \geq x$
$x \leq 9.25$ or $x \leq \frac{37}{4}$

Graphing Notes:

1. For $x < -25$: Draw an open circle at $-25$ on the number line, then shade all values to the left of $-25$.
2. For $x \leq 9.25$: Draw a closed circle at $9.25$ (or $\frac{37}{4}$) on the number line, then shade all values to the left of this point.

Answer:

1. Solution for $\frac{1}{5}x + 14 < 9$: $\boldsymbol{x < -25}$
2. Solution for $-193 \leq -12x - 82$: $\boldsymbol{x \leq \frac{37}{4}}$ (or $\boldsymbol{x \leq 9.25}$)