Question

quiz 2.4 2.5 score _/60 algebraic solution & sketch the solution on the number line 2. $\frac{1}{6}x + 2 leq \frac{3}{4}x - 2$

Explanation:

Step1: Move x - terms to one - side

Subtract $\frac{1}{6}x$ from both sides:
$2\leq\frac{3}{4}x-\frac{1}{6}x - 2$.
Then add 2 to both sides: $4\leq\frac{3}{4}x-\frac{1}{6}x$.

Step2: Find a common denominator for x - terms

The common denominator of 4 and 6 is 12. So $\frac{3}{4}x-\frac{1}{6}x=\frac{9}{12}x-\frac{2}{12}x=\frac{9x - 2x}{12}=\frac{7}{12}x$.
The inequality becomes $4\leq\frac{7}{12}x$.

Step3: Solve for x

Multiply both sides by $\frac{12}{7}$ (since $\frac{12}{7}>0$, the inequality sign remains the same).
$x\geq4\times\frac{12}{7}=\frac{48}{7}$.

Answer:

The solution of the inequality is $x\geq\frac{48}{7}$. On the number - line, draw a closed circle at $\frac{48}{7}\approx6.86$ and shade to the right.