Grade 9 · Verify an algebraic solution · 68 of 750
Verify an algebraic solution · practice 8
Solve 3x + (12) = -17, then check by substitution. 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 + (12) = -17, then check by substitution.
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Subtract the constant from both sides before dividing by the coefficient.
Work through the reasoning
Step 1
Translate the givens
Subtract 12 from both sides: 3x = -17 − (12) = -29.
Step 2
Calculate with the model
Because 3 is nonzero, divide both sides: x = -29/3 ≈ -9.66667. Keep the fraction for an exact check.
Step 3
Check and interpret
Substitute the exact value: 3 × (-29/3) + (12) = -29 + (12) = -17. Equality is preserved.
The answer
x = (-17 − (12))/3 = -29/3 ≈ -9.66667.
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.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
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The mathematical idea
Solving an equation finds an input that makes two expressions equal. Subtracting the same constant from both sides and dividing both sides by the same nonzero coefficient preserve the solution set. Substitution in the original equation checks the result. Starting quantities: Coefficient a = 3; Constant b = 12; Right side c = -17.
ax + b = c → ax = c−b → x = (c−b)/a
03 · Reflect and transfer
Explain what changes and why.
Why is substituting the exact fraction preferable to checking a rounded decimal?
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.