Solve 2x + 5 = 17
Undo addition first, then divide by the coefficient of x. Substituting x = 6 recovers the original right-hand side.
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Solve 3x − 7 = 14
A two-step linear equation: move the constant, then divide. The check is 3(7) − 7 = 14.
Solve x² − 5x + 6 = 0
Standard form is already ax² + bx + c = 0. The discriminant is 1, so there are two real roots: 2 and 3.
Solve x² − 9 = 0
Rewrite as x² = 9, or factor the difference of squares. Both real solutions are required.
Derivative of x³ + 2x
Bring each exponent down and reduce the power by 1. The derivative of 2x is the constant 2.
Indefinite Integral of x²
Reverse the power rule. Do not forget + C; functions that differ by a constant share a derivative.
Area of a Circle with Radius 5
A = πr². With r = 5, A = 25π. Do not substitute a decimal for π unless the problem asks for an approximation.
Hypotenuse of a 3-4 Right Triangle
a² + b² = c². 9 + 16 = 25, so c = 5. The theorem applies only when one angle is 90°.
sin(30°) Exact Value
On the unit circle, 30° corresponds to y-coordinate 1/2. In a 30-60-90 triangle, opposite/hypotenuse is also 1/2.
Mean of 2, 4, 6, and 8
Add 2 + 4 + 6 + 8 = 20, then divide by 4. The mean uses every value, so outliers would pull it.
Distance at 40 Miles per Hour for 2 Hours
Translate the sentence into d = rt. Substitute r = 40 and t = 2 to get 80 miles. Units stay in miles.
Solve x + y = 5 and x − y = 1
Add the two equations to get 2x = 6, so x = 3. Substitute into x + y = 5 to find y = 2.