Grade 7 · Reverse order for negative division · 14 of 750
Reverse order for negative division · practice 2
Solve -5x ≤ -13, 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 -5x ≤ -13, 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 -5, which is negative; it is safe to divide because it is nonzero.
Step 2
Calculate with the model
Divide both sides by -5: x ≥ -13/-5. The negative divisor reverses order.
Step 3
Check and interpret
At x = -13/-5, the product is exactly -13, so the boundary belongs. A test point one unit above the boundary reduces the left side by 5.
The answer
x ≥ -13/-5 (boundary ≈ 2.6).
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 = 5; Right-side bound = -13; 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.