Question

question 1-4
graph the solution to the inequality on the number line.
first select the type of line/arrow you want to draw and then drag it to the correct locations.
$\frac{1}{4}x > - 1$ and $-2(x - 1)geq4$

Explanation:

Step1: Solve the first - inequality

Solve $\frac{1}{4}x>-1$. Multiply both sides by 4 to get $x > - 4$.

Step2: Solve the second - inequality

Solve $-2(x - 1)\geq4$. First, distribute the - 2: $-2x+2\geq4$. Then subtract 2 from both sides: $-2x\geq2$. Divide both sides by - 2 and reverse the inequality sign, we get $x\leq - 1$.

Step3: Find the intersection

The solution of the compound - inequality is the intersection of $x > - 4$ and $x\leq - 1$, which is $-4 < x\leq - 1$.

Step4: Graph on the number line

On the number line, we use an open circle at $x=-4$ (because $x > - 4$, not $x\geq - 4$) and a closed circle at $x = - 1$ (because $x\leq - 1$), and draw a line segment between them.

Answer:

On the number line, use an open circle at $x=-4$ and a closed circle at $x = - 1$ and draw a line segment between them.