Question

solve the compound inequality and graph the solution. 3≤7x - 4<10. the solution is x <. 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 all parts of \(3\leq7x - 4\lt10\). For \(3\leq7x - 4\), we get \(3 + 4\leq7x-4 + 4\), which simplifies to \(7\leq7x\). Then divide both sides by 7: \(\frac{7}{7}\leq\frac{7x}{7}\), so \(1\leq x\).

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

For \(7x - 4\lt10\), add 4 to both sides: \(7x-4 + 4\lt10 + 4\), which gives \(7x\lt14\). Divide both sides by 7: \(\frac{7x}{7}\lt\frac{14}{7}\), so \(x\lt2\).

Step3: Combine the solutions

The solution of the compound inequality is \(1\leq x\lt2\). 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) and the line between them.

Answer:

The solution is \(1\leq x\lt2\). The correct graph has a closed circle at 1 and an open circle at 2 with the line segment between them. Without seeing the exact labels of the graphs, the description of the correct graph is a number - line with a closed dot at 1, an open dot at 2, and a line connecting them.