Question

which is a correct first step in solving $5 - 2x < 8x - 3$?
$5 < 6x - 3$
$2 - 2x < 8x$
$3x < 8x - 3$
$5 < 10x - 3$

Explanation:

Step1: Recall inequality properties

To solve \(5 - 2x < 8x - 3\), we can use the addition property of inequalities (adding the same term to both sides preserves the inequality). We want to get all \(x\)-terms on one side or constants on one side. Let's add \(2x\) to both sides.
\[
5 - 2x+ 2x< 8x - 3 + 2x
\]

Step2: Simplify both sides

Simplifying the left - hand side: \(-2x + 2x=0\), so the left - hand side becomes \(5\).
Simplifying the right - hand side: \(8x+2x = 10x\), so the right - hand side becomes \(10x-3\).
So we get \(5 < 10x - 3\).

Answer:

\(5 < 10x - 3\)