Question

the quadratic formula.
27.b
solve each inequality.
$20x + 8 - 4(7x + 2) < 4$
answer
example: $x < -3$; $3 < x < 7$; $x > 7$

Explanation:

Step1: Simplify the left - hand side

First, expand the expression \(-4(7x + 2)\) using the distributive property \(a(b + c)=ab+ac\). Here \(a=-4\), \(b = 7x\) and \(c = 2\), so \(-4(7x+2)=-28x-8\).
Then the inequality \(20x + 8-4(7x + 2)\lt4\) becomes \(20x + 8-28x-8\lt4\).
Combine like terms: \(20x-28x=-8x\) and \(8 - 8 = 0\), so the inequality simplifies to \(-8x\lt4\).

Step2: Solve for \(x\)

To solve for \(x\), we divide both sides of the inequality \(-8x\lt4\) by \(-8\). When we divide or multiply both sides of an inequality by a negative number, the direction of the inequality sign changes.
So \(\frac{-8x}{-8}\gt\frac{4}{-8}\) (note the change in the inequality sign).
Simplifying, we get \(x\gt-\frac{1}{2}\).

Answer:

\(x\gt-\frac{1}{2}\)