Question

u2l19 practice - solutions to inequalities in one variable
which graph represents the solution to $5 + 8x < 3(2x + 4)$?

Explanation:

Step1: Expand the right - hand side

Expand \(3(2x + 4)\) using the distributive property \(a(b + c)=ab+ac\). So, \(3(2x + 4)=6x+12\). The inequality becomes \(5 + 8x<6x + 12\).

Step2: Subtract \(6x\) from both sides

Subtracting \(6x\) from both sides of the inequality \(5 + 8x<6x + 12\) gives \(5+8x-6x<6x + 12-6x\). Simplifying, we get \(5 + 2x<12\).

Step3: Subtract \(5\) from both sides

Subtract \(5\) from both sides: \(5 + 2x-5<12-5\). This simplifies to \(2x<7\).

Step4: Divide both sides by \(2\)

Divide both sides of \(2x<7\) by \(2\). We have \(x<\frac{7}{2}=3.5\).

On a number line, for the inequality \(x < 3.5\), there is an open circle at \(x = 3.5\) (because the inequality is strict, i.e., \(x\) is not equal to \(3.5\)) and the line extends to the left.

Answer:

The second option (the number line with an open circle at \(3.5\) and the line extending to the left) represents the solution.