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Published on October 11, 2026
Solve the rational equation G/S = Y/2 for the variable S by cross-multiplying and isolating S to get S = 2G/Y.
This problem involves determining the correct system of inequalities based on a graph showing a shaded region bounded by a solid parabola and a dashed absolute value function. The solution requires analyzing the line types (solid vs. dashed) to determine strict or non-strict inequalities and identifying the equations of the boundary curves.
Simplify x/(x − 7) + (4x − 1)/(x − 7) by adding the numerators and keeping the common denominator. The result is (5x − 1)/(x − 7), where x ≠ 7.
Prove algebraically that the expression n^2 - 2 - (n - 2)^2 is always an even number by expanding the brackets and factoring out a 2.
Determine that the rational equation (y-1)/(1-y)=1 has no solution because the denominator is the negative of the numerator, making the left side equal -1.
This problem involves solving the cubic equation 2x^3 + 2x^2 - 24x = 0 by factoring out the greatest common factor and then factoring the resulting quadratic expression.