What Is The First Step In Solving 5 2x 8x 3?

Stuck staring at 5 – 2x < 8x – 3? You’re not the only one. The fastest way out is to herd all the x’s to one pasture and the numbers to the other. Start by tossing 2x onto both sides.

What’s the core issue here?

You’re staring down a linear inequality, not a run-of-the-mill equation. The entire game is isolating x so the solution pops out cleanly. The opening move is always about corralling every x term onto one side and parking all the constants on the opposite side. That keeps the math honest and helps you dodge sign flip disasters.

How do I actually solve it?

Grab the first tool from your kit: add 2x to both sides. This nudges every x term to the right side while leaving the constants on the left.

1. Add 2x to both sides.
   • 5 – 2x + 2x < 8x – 3 + 2x
   • Boils down to 5 < 10x – 3
2. Now toss 3 onto both sides.
   • 5 + 3 < 10x – 3 + 3
   • Simplifies further to 8 < 10x
3. Finally, divide both sides by 10.
   • 8/10 < (10x)/10
   • Leaves you with 0.8 < x, or x > 0.8

What if that approach bombs?

• Option 1 – Reverse the herd. Start by shooing the 8x off to the left instead: subtract 8x from both sides first. 5 – 2x – 8x < –3 → 5 – 10x < –3. Then subtract 5 and divide by –10 (remember to flip the inequality sign).
• Option 2 – Sweep out fractions early. Got fractions in the mix? Multiply every term by the common denominator before you even think about isolating x.
• Option 3 – Draw the lines. Fire up any graphing tool (Desmos, GeoGebra, TI-84) and plot both sides as straight lines. The intersection point gives you the solution directly.

How can I avoid messing this up in the future?

• Mind the sign flip. Any time you move a term across the inequality line, flip its sign. The classic rookie mistake? Forgetting to flip when you divide by a negative number.
• Double-check your answer. Slide your solution back into the original inequality. For x > 0.8, try 1; it should satisfy 5 – 2(1) < 8(1) – 3 → 3 < 5, which checks out.
• Drill the first move. Turn every inequality into a quick reflex: “x’s left, numbers right.” Repeat until it feels like second nature.

According to the Math is Fun guide and the Khan Academy linear-inequality module, the opening step is almost always to gather variable terms on one side of the inequality.