How to solve 2(x+5)=18 and find x: a quick walkthrough of a linear equation

What this little equation teaches about math thinking

Math on the HSPT math section isn’t just about plugging numbers into a box. It’s about following a clean line of reasoning, keeping the sides balanced, and letting the structure of the problem reveal the answer. Here’s a simple, concrete example that sheds light on how to approach similar questions with confidence.

The question you’ll sometimes see (and yes, it’s exactly the kind of thing that shows up in the test’s math portion)

Solve for x: 2(x + 5) = 18

A. 2

B. 4

C. 6

D. 8

If you’re skimming, you might miss what’s really happening here. But the right approach is straightforward: expand, isolate, and verify. Let me explain how that works step by step.

Step 1: Expand the left side so the equation is easier to read

Take the expression 2(x + 5). The distributive property says you multiply 2 by each part inside the parentheses. So:

2(x + 5) becomes 2x + 10.

Now the equation looks like:

2x + 10 = 18

Distributive property, in a nutshell, is like spreading a small idea to see the whole picture. It helps you avoid a trap where you try to stare at x inside a little pocket and pretend the rest isn’t there.

Step 2: Get the x term by itself

Next, you want to move the 10 to the other side so the equation keeps only the x-term on the left. Subtract 10 from both sides:

2x + 10 − 10 = 18 − 10

which simplifies to:

2x = 8

Balancing both sides is the heart of solving linear equations. The goal is to “undo” whatever you did to the left side, so you keep everything in harmony.

Step 3: Solve for x

Now we just need to isolate x. Since 2x means 2 times x, divide both sides by 2:

(2x)/2 = 8/2

x = 4

That’s the answer. If you substitute back into the original equation, you’ll see it checks out:

2(4 + 5) = 2 × 9 = 18, which matches the right side.

Why this approach works (and how to see similar problems clearly)

• The core moves are consistent: distribute, then collect terms, then isolate the variable. If you memorize the pattern, you can recognize the structure of many HSPT math questions quickly.

• The distributive property is your ally. It tells you exactly how to open up expressions like 2(x + 5) so you can work with plain x terms.

• Keeping the sides balanced is a powerful habit. Every operation you perform on one side you perform on the other. It’s the most reliable way to avoid silly mistakes.

Common traps (and how to dodge them)

• Forgetting the distribution: If you skip the step of turning 2(x + 5) into 2x + 10, you’ll likely end up with the wrong path. Always expand first when you see a coefficient outside parentheses.

• Skipping the subtraction step: After expansion, you should move constants away from the x-term. If you jump to dividing or something else, you miss the straightforward path.

• Mixing up operations on both sides: If you add 10 to one side but not the other, you’ll throw off the balance and get the wrong x value.

• Not checking your answer: Substituting x back into the original equation is a quick way to confirm you didn’t slip up somewhere. It’s a tiny extra step that saves bigger headaches later.

Translating this to other kinds of problems you’ll encounter

• When you see something like a number outside parentheses multiplying a binomial, start by distributing. It’s almost always the right first move.

• If the expression has a constant term on the same side as x, think about moving constants to the opposite side to isolate x. That often means adding or subtracting a fixed number on both sides.

• If you encounter fractions, multiply through to clear denominators before proceeding. The logic is the same: simplify, then isolate, then verify.

A handy real-life analogy to keep the logic tangible

Think of solving an equation like balancing a budget. Suppose you earn 2x dollars from your side hustle and you get a fixed 10 dollars as a bonus. If you know the total income is 18 dollars, you first “expand” your expectations to include both x and the fixed bonus. Then you subtract the fixed portion to see what remains for the variable part. Finally, you divide the remaining amount by 2 to figure out how much each unit of x contributes. The steps feel natural because you’re trying to equalize both sides of a “deal.”

Different tones, same core idea

You’ll often hear people describe algebra as a toolkit. The trick is to keep the tools clean and the plan simple. The steps you used here aren’t special tricks; they’re just the right moves for this kind of puzzle. And that’s exactly how you approach other problems on the HSPT math section: recognize the pattern, apply the right property, and verify.

A few tips to keep you moving smoothly on test day

• Read slowly once, then read again with a plan. The first pass helps you spot the structure (is there a parenthesis? a distribution? a fraction?).

• Mark each operation you perform on both sides. It’s a mental habit that reduces errors.

• If a question feels sticky, pause and re-state the aim: you want to isolate x. Then pick the simplest path to that goal.

• Don’t let answer choices derail your thinking. Sometimes you can check quickly by plugging in a couple of options to see which fits, but with clean steps, you’ll usually converge to the right answer on the first try.

Why this matters for the broader HSPT math journey

This kind of problem—where you expand, balance, and isolate—is a microcosm of algebraic thinking you’ll rely on across the test. It trains you to keep track of the variable’s “home” and to respect the equality on both sides. When you’re juggling multiple steps, quick mental checks like “did I distribute all the way?” or “did I cancel the constant on both sides?” become second nature.

A quick check-in for confidence

Let me phrase it plainly: x = 4 is correct because it makes the left side equal the right side in the original equation. If you replace x with 4 and do the math, you’ll get 18 on both sides. There’s a neat clarity in seeing that balance come together.

Closing thoughts—staying curious and precise

If you enjoy solving problems that unfold logically, you’ll likely find the HSPT math section both fair and engaging. The key is to stay curious about why each step works, not just how to perform it. That mindset turns a single problem into a small victory and builds the momentum you want for the next challenge.

So, next time you’re faced with something like 2(x + 5) = 18, remember the three moves: expand, balance, solve. It’s a rhythm you can carry from question to question, from one topic to the next, with a steady growing sense of mastery. And who knows—the way you think through a simple equation might just spill over into a tougher scenario later, making the whole math journey feel a little less intimidating and a lot more doable.