How to solve 5x - 10 = 0 and find x the easy way

A simple equation, a clean path, and a little confidence—that’s all you need to crack this kind of HSPT math item. If you’re scanning through a set of questions and one pops up that looks like a maze of symbols, you’re not alone. The truth is, many math items in the HSPT section boil down to a single idea: isolate the variable. Let me walk you through a concrete example, then widen the lens a bit so you can see how this approach fits other questions you’ll encounter.

A concrete question to anchor the idea

Here’s a typical starter item you might see:

If 5x - 10 = 0, what is the value of x?

A. 1

B. 2

C. 3

D. 5

The correct answer is 2. To see why, you just need to isolate x. Let’s do it step by step, in a way that keeps the math clean and the thinking honest.

Step 1: Read the equation and spot the inverse operations

The equation is 5x - 10 = 0. The goal is to get x by itself on one side. The terms around x are -10 and the multiplication by 5. To undo those operations, you’ll do the opposite moves: add or subtract to move constants, and divide to remove the coefficient in front of x.

Step 2: Remove the constant term on the left

Add 10 to both sides. This is a standard move: what you add to one side, you add to the other. You’re keeping the balance of the equation intact while moving toward a simpler form.

5x = 10

Step 3: Undo the multiplication by 5

Divide both sides by 5. This step strips away the coefficient, leaving x by itself.

x = 10 / 5 = 2

Step 4: Quick check (a little pressure-free verification)

If x really equals 2, plug it back into the original equation: 5(2) - 10 = 10 - 10 = 0. The left side matches the right side, so the solution checks out. Substitution is a tiny, reliable parachute you can use whenever you’re unsure.

Two ways to see it: a faster path and a solid backup

If you love a shortcut, you can notice a neat factorization right away. The expression 5x - 10 can be factored as 5(x - 2). Setting the whole thing equal to zero, you apply the zero-product rule. Since 5 is never zero, you’re left with x - 2 = 0, which gives x = 2. This is a quick route, especially when you’re scanning a few problems in a row.

If you’re more comfortable sticking with the equation-as-a-balance idea, the first method—adding 10 and then dividing by 5—works just as well. The two roads meet at the same answer, and choosing the one that feels simplest is a smart move rather than a big struggle.

Why this matters beyond a single item

The approach you used here—identify inverse operations, perform them on both sides, and verify the result—applies to a lot of HSPT math items. You’ll see:

• Linear equations where the goal is to isolate a single variable

• Equations that mix terms in y or another letter with constants

• Quick checks to avoid careless mistakes

This isn’t about memorizing a trick so much as embracing a reliable method. When you treat algebra as a process of balancing and undoing operations, problems become predictable, not mystifying.

Common missteps and how to sidestep them

Even with a clear plan, it’s easy to slip. Here are a few frequent stumbling blocks and simple fixes:

• Forgetting to apply the same operation on both sides

The moment you move a term, you must do it to both sides. If you skip that, the equation loses its truth.

• Mixing up signs

Subtracting and adding can get tangled fast. If you’re not sure, write it out in a tiny, two-column mirror: left side, right side. Keep the operation in sync.

• Jumping to the answer without checking

It’s tempting to glide to a choice, especially under time pressure. Don’t skip the post-solve check. A quick substitution confirms your result and reinforces the habit.

• Overreliance on a calculator

For many HSPT items, mental math or straightforward arithmetic is enough. In situations where you do reach for a calculator, double-check that you’re applying the calculator to the right side and not skipping a step.

Carrying the method into broader HSPT math topics

This kind of equation work is a microcosm of math you’ll see in various formats on the HSPT:

• Solving for a variable in simple linear equations

• Recognizing when a problem factors, and using the zero-product rule

• Substituting a value to verify a solution quickly

• Keeping an eye on signs and the balance principle

If you map these skills onto a handful of problems, you’ll likely see a rhythm: identify what needs to be moved, apply the inverse operation, simplify, and check. That rhythm is exactly what helps you stay calm and precise when your mind feels a bit rattled by time constraints.

A mental warm-up you can try anywhere

Think of a balance scale you’ve used at home or in class. If there’s a weight on one side and you want to know what amount on the other side will bring the scale back to level, you’re doing the same thing as solving for x. You move the weights around with inverse moves until the scale is level. The same idea is at work in the equation we explored.

Here’s a small, practical routine you can try on a few problems in a row:

• Look for a constant term to move to the other side.

• Move it with a plus or minus, so the equation readjusts cleanly.

• Divide or multiply to isolate the variable.

• Check by substitution.

That flow is friendly to the brain and surprisingly effective, especially when the questions stack up.

A note on tone, pace, and confidence

When you’re approaching a problem like this, a calm, conversational pace helps. Don’t rush to the answer. Let your eyes rest on the equation, identify the inverse moves, and confirm with a quick check. Confidence grows when your steps are deliberate and transparent—even in a test setting.

If you’re thinking about how to approach a batch of similar questions, here are a few quick mind-tricks that don’t feel like tricks at all:

• Label the operations clearly in your head before you perform them—“add, then divide,” or “factor and set each factor to zero.”

• Use the simplest form you can reach in a single line; don’t overcomplicate.

• When in doubt, re-check by plugging the result back into the original equation. It’s an honest way to confirm you didn’t miss a sign or mix up a term.

Why one correct answer matters—and how to spot it quickly

In multiple-choice settings, you can use the options to sanity-check. In this example, if you guessed x = 2 and you want to be confident, you can test the nearby choices. For instance, try x = 1:

5(1) - 10 = -5, not 0. Try x = 3:

5(3) - 10 = 5, not 0. Both fail to satisfy the equation, which reinforces that x = 2 is the only valid solution. This kind of elimination helps when you’re racing the clock and the nerves start to creep in.

A final word about the bigger picture

Math, including the kinds of questions you’ll see here, rewards clarity and a steady approach. It’s less about dazzling tricks and more about understanding the logic of equations and about training your brain to handle variables with confidence. The move from 5x - 10 = 0 to x = 2 is a tiny journey, but it’s a journey that teaches a lasting habit: treat the equation as a balance, keep your moves consistent, and check your work.

If you keep that mindset, you’ll find many HSPT math items start to feel almost like familiar puzzles. Not easy in a blink, but approachable. Not a mystery, either, once you’ve got a reliable method on your side.

To sum it up

• The problem 5x - 10 = 0 leads you to x = 2.

• You can reach that result by adding 10 to both sides and then dividing by 5, or by factoring as 5(x - 2) = 0 and setting x - 2 = 0.

• Substitution confirms the solution is correct.

• This approach—identify inverse operations, apply them to both sides, and verify—maps to many HSPT math items, so practicing it a few times helps your confidence go up without extra stress.

If you enjoyed walking through this problem, you’ll likely find similar reasoning handy across the HSPT math section. The core idea remains the same: hold the equation steady, untangle it with the simplest moves, and trust your steps. That’s a skill you can carry far beyond any single item, turning quiet competence into a reliable math instinct.