Question

solve the following inequality and graph the solution.
$3(x - 2) < 5(2x - 1)$

a. $x > \square$
b. $x < \square$
c. $x \geq \square$
d. $x \leq \square$

choose the correct graph.
a. number line with arrow to left ending at 5
b. number line with arrow to right starting at 5
c. number line with arrow to right starting at 5, closed dot
d. number line with arrow to left ending at 5, closed dot

Explanation:

Step1: Expand both sides

$3x - 6 < 22x - 11$

Step2: Move x terms to left side

$3x - 22x < -11 + 6$

Step3: Simplify both sides

$-19x < -5$

Step4: Divide by -19, reverse inequality

$x > \frac{5}{19}$

Answer:

The solution to the inequality is $\boldsymbol{x > \frac{5}{19}}$. The corresponding graph is Option C (a number line with an open circle at $\frac{5}{19}$ and a blue arrow pointing to the right, covering all values greater than $\frac{5}{19}$).