Question

unit 2 lessons 18 to 20 swyk
which graph represents the solution to $\frac{1}{4}x + 3 < \frac{7}{8}x - 2$

Explanation:

Step1: Eliminate the fraction

Multiply each term of the inequality \(\frac{1}{4}x + 3<\frac{7}{8}x-2\) by \(8\) (the least - common multiple of \(4\) and \(8\)) to get \(2x + 24<7x-16\).

Step2: Move the \(x\) - terms to one side and constants to the other side

Subtract \(2x\) from both sides: \(24<7x - 2x-16\), which simplifies to \(24<5x-16\). Then add \(16\) to both sides: \(24 + 16<5x\), so \(40<5x\).

Step3: Solve for \(x\)

Divide both sides by \(5\): \(\frac{40}{5} 8\).

Answer:

The graph with an open circle at \(8\) and an arrow pointing to the right (the second option from the bottom in the given set of graphs).