A clever application of the distributive property to solve a multi-step equation | Khan Academy

Summary

This video demonstrates how to solve a multi-step linear equation with fractions by using the distributive property to clear the denominators. The presenter walks through each step of the simplification and verification process, ultimately arriving at the solution for x.

Highlights

Introduction to the Equation and Strategy00:00:00

The video starts with the equation 3/4x + 2 = 3/8x - 4. To simplify solving, the presenter suggests eliminating fractions by multiplying both sides of the equation by a common number.

Choosing the Multiplier to Eliminate Fractions00:00:33

The best number to multiply by is the least common multiple of the denominators (4 and 8), which is 8. Multiplying by 8 will convert all fractional terms into whole numbers.

Applying the Distributive Property and Simplifying00:01:05

Multiplying both sides by 8: (8 * 3/4x) + (8 * 2) = (8 * 3/8x) - (8 * 4). This simplifies to 6x + 16 = 3x - 32.

Gathering x Terms and Constants00:01:57

To get all x terms on the left, subtract 3x from both sides: 3x + 16 = -32. To get constants on the right, subtract 16 from both sides: 3x = -48.

Solving for x00:03:02

Divide both sides by 3 to isolate x: x = -48 / 3, which results in x = -16.

Verifying the Solution00:03:30

The presenter substitutes x = -16 back into the original equation to check the answer. 3/4(-16) + 2 = -12 + 2 = -10. And 3/8(-16) - 4 = -6 - 4 = -10. Since both sides equal -10, the solution x = -16 is correct.