Question

solve the linear inequality. other than \\( \varnothing \\), graph the solution set on a number line.\\( 8(x + 3) \leq 7(x + 4) + x \\)select the correct choice below and, if necessary, fill in the answer box to complete your choice.\\( \boldsymbol{\circ} \\) a. the solution set in interval notation is \\( \square \\). (simplify your answer. use integers or fractions for any numbers in the expression. type your answer in interval notation.)\\( \boldsymbol{\circ} \\) b. the solution set is \\( \varnothing \\).

Explanation:

Step1: Expand both sides

Expand the left - hand side: \(8(x + 3)=8x+24\)
Expand the right - hand side: \(7(x + 4)+x=7x + 28+x=8x+28\)
So the inequality becomes \(8x + 24\leq8x+28\)

Step2: Subtract \(8x\) from both sides

Subtract \(8x\) from both sides of the inequality \(8x + 24\leq8x+28\), we get \((8x - 8x)+24\leq(8x - 8x)+28\), which simplifies to \(24\leq28\)

Since \(24\leq28\) is always true, the solution set includes all real numbers. In interval notation, the set of all real numbers is \((-\infty,\infty)\)

Answer:

A. The solution set in interval notation is \((-\infty,\infty)\)