Grade 7 · Reverse order for negative division · 43 of 750
Reverse order for negative division · practice 5
Solve 3x ≤ 8, including the boundary. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
Solve 3x ≤ 8, including the boundary.
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A starting point
When dividing by a negative number, reverse the comparison sign.
Work through the reasoning
Step 1
Translate the givens
The coefficient is 3, which is positive; it is safe to divide because it is nonzero.
Step 2
Calculate with the model
Divide both sides by 3: x ≤ 8/3. The positive divisor preserves order.
Step 3
Check and interpret
At x = 8/3, the product is exactly 8, so the boundary belongs. A test point one unit below the boundary reduces the left side by 3.
The answer
x ≤ 8/3 (boundary ≈ 2.66667).
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
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Watch the relationship
PausedHD animation studio
From experiment to screen.
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The mathematical idea
An inequality describes a set of inputs rather than just one answer. Dividing by a negative coefficient reverses the direction of comparison because it reverses order on the number line. The boundary remains included for a non-strict inequality. Starting quantities: Coefficient magnitude = 3; Right-side bound = 8; Coefficient sign: −1 or +1 = 1.
ax ≤ b; x ≤ b/a if a>0, x ≥ b/a if a<0
03 · Reflect and transfer
Explain what changes and why.
How would the endpoint marker change if the original comparison were strict?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.