NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
← Back to practice

Simplifying linear expressions

Wide tables scroll horizontally. For detailed working, you may prefer a larger screen.

Required skills (click to reveal)

A school in Darwin is ordering art supplies. The order includes 13 boxes of coloured pencils and 47 boxes of paintbrushes.

Each box of coloured pencils contains x pencils, and each box of paintbrushes contains 2x + 3 brushes. The total number of art items ordered is given by the expression 13x + 47(2x + 3).

Simplify this linear expression using the distributive, associative, and commutative properties. Show all steps and provide the exact simplified form as a single algebraic expression with integer coefficients and constant.

Final answer must be in the form of a simplified expression.

Concept illustrations

These are separate worked examples of related concepts, not a diagram of this question. Their values and dimensions do not describe your question.

Combining like terms as equal tiles. Each tile represents x. Three x-tiles and two x-tiles make five x-tiles. A constant tile represents a different quantity.xxxxx3x2x3x + 2x = 5x
Each tile represents x. Three x-tiles and two x-tiles make five x-tiles. A constant tile represents a different quantity.
Distributive law as a rectangle. A rectangle of height 3 and total width x + 4 splits into areas 3x and 12. Therefore 3(x + 4) = 3x + 12. Algebraic lengths are schematic.x433x123(x + 4) = 3x + 12
A rectangle of height 3 and total width x + 4 splits into areas 3x and 12. Therefore 3(x + 4) = 3x + 12. Algebraic lengths are schematic.

Press Start when ready. Time includes time spent in another tab. Submit your answer before opening a help panel for a timed rank.

00:00
0 wordsOnly your numerical final answer or selected MCQ option is checked. Scratch working is not graded.

Report a problem or suggest an improvement

My notes — optional, not graded 0 words

Notes and scratch working stay in this browser and are linked to this question version. They are not graded or included in feedback. On shared devices, other people using this browser may see them.

For this question only. Your full notebook is on the dashboard.

Notes save in this browser. Download a copy to keep them elsewhere.

Report a problem or suggest an improvement

Your observations help improve this question. You can report an issue or recommend a better explanation, visual or experience.

0 words

The report includes your message and question/version details. Saved profile details, answers, notes and attempt history are not automatically attached. Leave out names and contact details, and check screenshots for personal information and embedded metadata.

Attachments may contain personal information. Review them before sharing. Logs collect only event codes and timestamps after you enable them. Download the ZIP to keep a copy, then attach it to an email if you choose.

Formula and explanation (click to reveal)

Opening this before your first submission makes the attempt practice only.

Formula

Explanation

Worked solution and answer (click to reveal)

Opening this before your first submission makes the attempt practice only.

Worked solution

  1. The expression given is 13x + 47(2x + 3). This represents the total number of art items ordered, with 13 boxes of coloured pencils (each containing x pencils) and 47 boxes of paintbrushes (each containing 2x + 3 brushes).
  2. Apply the distributive property to expand 47(2x + 3). Multiply 47 by each term inside the parentheses: 47 * 2x = 94x and 47 * 3 = 141.
  3. Substitute the expanded terms back into the expression: 13x + 94x + 141.
  4. Use the commutative property of addition to rearrange the terms: 13x + 94x + 141 becomes 94x + 13x + 141.
  5. Use the associative property to group the like terms: (94x + 13x) + 141.
  6. Add the coefficients of x: 94 + 13 = 107. So, 94x + 13x = 107x.
  7. The simplified expression is now 107x + 141.
  8. Verify the simplification by checking the original structure: 13x + 47(2x + 3) = 13x + 94x + 141 = 107x + 141.
  9. Confirm all coefficients and constants are integers, and the expression is in standard linear form with integer coefficients and constant.
  10. The expression 107x + 141 is fully simplified and matches the required form.

Reference answer: 107x + 141

Alternative methods (click to reveal)

Shortcuts are shown only when applicable. Check the conditions before using one.

Earlier attempts for this question

#Date / timeYour answerResultSecondsHelp revealedRank
History stays in this browser when storage is available. Export it to your shared Drive folder and import it on another computer.
Worksheet details

Naming pattern: Topic_Grade_Complexity_YYYYMMDD_HH24MISS.html

Validation compares your answer with the generated reference. The model's reference can be wrong. Time ranks use an estimated student solving time, not a measured benchmark or a comparison with other students. An incorrect answer receives no speed rank.

NavGanitMate privacy & saved work

Saved in this browser. Your profile preferences, answers, practice history and notes are stored here when browser storage is available. They are not automatically uploaded to our servers. People sharing this browser may see saved work; changing the learner name does not create a separate private account. A nickname is enough.

Keep copies of important work. Clearing browser data, private browsing or changing browser or device can mean losing saved work. Download notes and export history separately. Downloads are copies of the selected content, not a complete account backup; not every format can be imported to restore your work. Keep these files somewhere private.

Visiting the website. Cloudflare helps deliver and protect this site and processes connection information such as IP addresses and requested pages. Server error logs may also contain request details. Security features may use cookies. This is separate from your browser-saved learning records. Cloudflare privacy information.

A parent-connection reminder uses a local list of up to five completed question IDs for this browser profile and a tab-session dismissal marker. Reminder activity is not uploaded and practice remains available.

Sharing feedback is your choice. A report includes your message and question/version details. Your saved profile, answers and notes are not automatically attached. Files you select can reveal personal details or contain embedded metadata: check and redact them before sharing. Diagnostic event codes and timestamps are included only after you enable logging. Sending email shares your message and attachments with the recipient and email providers. A download alone sends nothing to us. Website feedback delivery may be unavailable; only a confirmed receipt indicates it was received.