Question

solve the compound inequality and graph the solution. 3≤7x - 4<10. the solution is x < 10. the solution is all real numbers. there is no solution. graph the solution. choose the correct graph below.

Explanation:

Step1: Solve the left - hand side of the compound inequality

Add 4 to both sides of $3\leq7x - 4$. We get $3 + 4\leq7x-4 + 4$, which simplifies to $7\leq7x$. Then divide both sides by 7, so $x\geq1$.

Step2: Solve the right - hand side of the compound inequality

Add 4 to both sides of $7x - 4<10$. We get $7x-4 + 4<10 + 4$, which simplifies to $7x<14$. Then divide both sides by 7, so $x < 2$.

Step3: Determine the solution set

The solution of the compound inequality $3\leq7x - 4<10$ is $1\leq x<2$. On a number - line, we have a closed circle at $x = 1$ (because $x$ can equal 1) and an open circle at $x = 2$ (because $x$ cannot equal 2) with a line segment between them.

Answer:

The solution is $1\leq x<2$. The correct graph would have a closed circle at 1 and an open circle at 2 with a line segment connecting them. Without seeing the exact labels of the graphs in detail, if we assume the standard number - line graphs with correct circle types and positions, the graph that has a closed circle at 1, an open circle at 2 and a line segment between them is the correct one.