Question

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

○ (-∞, 6)
○ (6, ∞)
○ ∅
○ (-∞, ∞)

Explanation:

Step1: Expand both sides

Expand the left - hand side: \(5(4x + 6)-4x=20x+30 - 4x=16x + 30\)
Expand the right - hand side: \(4(7 + 4x)-6=28+16x-6 = 16x+22\)
So the inequality becomes \(16x + 30<16x+22\)

Step2: Subtract \(16x\) from both sides

Subtract \(16x\) from both sides of the inequality \(16x + 30<16x+22\), we get \(16x-16x + 30<16x-16x+22\)
Simplifying, we have \(30 < 22\)

Since \(30<22\) is a false statement, there are no values of \(x\) that satisfy the inequality. So the solution set is the empty set \(\varnothing\)

Answer:

\(\varnothing\) (corresponding to the option with \(\varnothing\))