Solving 4x - 5 = 15 and finding that x equals 5

Crack the algebra puzzle in your HSPT math toolkit

If you’ve ever stared at a sentence like a riddle and thought, “What number are they hiding in here?” you’re not alone. The HSPT math section loves problems that look wordy at first but reveal a clean path once you translate them into numbers. Here’s a straightforward example that often appears in many forms: a number is multiplied by 4, then decreased by 5, and the result is 15. What’s the number?

Let’s walk through it together, step by step, so the process feels less mythical and more like a reliable routine you can reuse.

Turn words into a small equation

The first move is to name the unknown. Let the number be x. The phrase “multiplied by 4” means 4x. The phrase “decreased by 5” means minus 5. Put those ideas together, and the sentence becomes an equation:

4x − 5 = 15

If this looks a little abstract, think of it as a tiny balance: four copies of the unknown on one side, and some constant adjustments on the other. The key is to keep the operations in the right order and to remember that “decreased by 5” nudges the left side downward.

Isolate the variable, cleanly

Now, the goal is to get x by itself. That’s algebra 101, but it pays to treat it with the calm patience you’d use for a puzzle.

• Add 5 to both sides. The reason is simple: you want to undo the “−5” on the left. After doing the math, you get:

4x = 20

• Divide both sides by 4. This step strips away the multiplier and leaves x alone:

x = 5

That’s the solution. But the journey isn’t just about getting a number; it’s about trusting the method so you can apply it to similar problems faster in the future.

Check your answer

A quick check seals the deal. Substitute x back into the original expression:

4(5) − 5 = 20 − 5 = 15

The left side matches the given result, so the solution is consistent. Quick checks like this are mental shortcuts that save you time and avoid careless slips during the test.

Why this approach works for many HSPT-style questions

This little problem is a microcosm of a bigger pattern you’ll see often in the HSPT math section: a linear equation hidden in words. The steps you used here—translate, isolate, verify—form a reliable blueprint.

• Translate carefully. The language of a problem holds clues about which operations to perform. Words like “times,” “plus,” “minus,” “increased by,” and “decreased by” map directly to multiply, add, or subtract. Practicing this translation turns wordy sentences into crisp algebra.

• Isolate the variable. The goal in most of these problems is to move constants to the opposite side of the equation so the unknown sits alone. It’s not about memorizing a million tricks; it’s about a consistent, repeatable flow.

• Verify with substitution. A quick check can catch careless mistakes. If the numbers don’t play nice when you plug them back in, you know to re-examine your steps.

A few quick tips to apply this mindset broadly

• Start with what you know. If you see a letter like x with operations around it, write down the exact expression. Don’t rely on a mental shortcut you’re not sure about yet.

• Keep a tiny scratch pad routine. Jot the equation, then mark the operations you’ll perform on each side. This visual helps you avoid forgetting a minus sign or mixing up the order of operations.

• Look for a straightforward path. If the problem seems to spiral into a tangle, pause and reframe: what single operation would undo the last change? Often the answer is right there in front of you, just inverted.

• Use a quick check habit. A two-line substitution check can save you from a lot of grief. If you solve for x, plug it back in. If it doesn’t work, retrace your steps.

Common pitfalls to watch for on similar problems

Even smart test-takers trip over the same traps, especially when the wording gets slippery. A few things to watch:

• Forgetting to apply the same operation to both sides. If you add or subtract on one side, do it on the other side too.

• Failing to reverse the operations in the correct order. If you see a multiplication and a subtraction, you’ll typically undo subtraction first and then tackle multiplication, or vice versa depending on the structure. The safest route is to think in reverse: what would you need to do to get back to the original x?

• Misreading the statement. A small misread—like “multiplied by 4” versus “multiplied by 4 times something”—can throw off the whole setup. Slow, deliberate reading pays off.

• Overlooking the simplest check. The substitution step is tiny, but it’s incredibly powerful for confidence that you’re on the right track.

Anchoring this to real-world intuition

Imagine you’re organizing a small project with a handful of steps. You start with a number of pieces, you double them, then you take away a few pieces, and you’re left with a target count. Translating the story to a clean equation feels like writing a shopping list for your math project: it clarifies what you have and what you need to adjust to reach the goal. The HSPT isn’t about memorizing clever tricks as much as it is about building a sensible way to map stories to arithmetic.

Beyond one problem: what else you’ll encounter in the HSPT math section

The algebra-style problem you just solved is a doorway to other familiar terrains:

• Linear equations in one variable, where you isolate x by undoing additions and subtractions before dealing with multipliers or divisions.

• Basic geometry questions that hinge on area, perimeter, and simple relations using formulas you’ll recognize once you see the pattern.

• Fraction and ratio problems that ask you to combine parts to reach a whole, often with a clean algebraic route underneath.

• Word problems that compress a situation into a short algebraic tune. The trick is to listen for verbs that imply operations—times, divided by, increased by, decreased by, minus, plus.

If you want to reinforce this framework, many reputable sources offer drills that reinforce the exact skill you used here. Look for explanations that walk you through translating sentences into equations, then solving and verifying. Tools like Khan Academy, for instance, provide approachable lessons that mirror this logic, helping you build confidence without getting lost in complexity.

A tiny detour you might enjoy

While we’re talking about clear thinking, consider how this translates to everyday life. Suppose you’re planning a small budget for a trip or a group project. You know how much you start with, you apply some rule (like “every friend pays four times what I do”), then you adjust by removing a fixed amount for incidentals. The math doesn’t vanish when the athletes leave the court; it just becomes a practical way to distribute effort and keep your eye on the target total. It’s math in motion, not some far-off schoolroom exercise.

Bringing it home: a compact approach you can lean on

• Read the problem once, then twice. Let the unknown stand in for the part of the story that’s variable.

• Translate the sentence into a lean equation. Keep it simple: a single variable, a straightforward combination of operations.

• Solve with the classic undo sequence: isolate the variable by undoing each operation, moving step by step from the outermost action to the inner.

• Check by substitution. If the numbers fit, you’ve earned a clean victory.

• Build the habit. With each problem you encounter, you’re sharpening a precise, human way to think: curious, methodical, and ready to adapt.

Final thought

That little question about a number that’s4 times as big, then minus 5, ending up at 15, isn’t just a problem you’ll shrug off on the day of the test. It’s a blueprint for how to approach similar challenges with calm, confidence, and a clear plan. It’s the same method you’ll notice across a lot of HSPT math questions: read, translate, isolate, verify. Do it consistently, and you’ll see your speed and accuracy improve naturally.

If you’re curious to practice more, seek out similar word problems and give them a go. Use the same steps, and you’ll notice a pattern emerge—one that makes math feel less like a test and more like a language you’re fluent in. And that’s a momentum you can carry beyond the page, into classrooms, into daily life, and into every small decision that involves numbers.