Question

solve the linear inequality. other than \\( \emptyset \\), use interval notation to express the solution set and graph the solution set on a number line.\\( 5(4x + 6) - 4x < 4(7 + 4x) - 6 \\)\\( \bigcirc \\ (6, \infty) \\)\\( \bigcirc \\ \emptyset \\)\\( \bigcirc \\ (-\infty, 6) \\)\\( \bigcirc \\ (-\infty, \infty) \\)

Explanation:

Step1: Expand both sides

$5(4x+6)-4x = 20x + 30 - 4x = 16x + 30$
$4(7+4x)-6 = 28 + 16x - 6 = 16x + 22$
Inequality becomes: $16x + 30 < 16x + 22$

Step2: Subtract $16x$ from both sides

$16x + 30 - 16x < 16x + 22 - 16x$
Simplifies to: $30 < 22$

Step3: Evaluate the statement

$30 < 22$ is a false statement, so there are no solutions.

Answer:

$\emptyset$
(With the corresponding number line showing no highlighted values)