Solving Linear Equations Steps

The video tutorial explains how to solve an SAT math problem involving a proportion. The problem is set up as an equation with variables x and a. The solution involves cross-multiplying the terms, distributing them, and then isolating the variable a. The final solution is expressed as a = x/15. The tutorial provides a step-by-step approach to solving the equation, ensuring clarity in each step of the process.

What is the initial equation given in the SAT question?

• (x - a) / 7 = (x + A) / 8

• (x - a) / 8 = (x + A) / 7

• (x + a) / 7 = (x - A) / 8

• (x + a) / 8 = (x - A) / 7

What is the first step in solving the equation using cross-multiplication?

• Add 8 to both sides

• Subtract 7 from both sides

• Multiply both sides by 7 and 8

• Divide both sides by 7 and 8

After cross-multiplying, what is the expression obtained on the left side of the equation?

• 7 * x - 7 * a

• 7 * x + 7 * a

• 8 * x + 8 * a

• 8 * x - 8 * a

What is the expression obtained on the right side of the equation after cross-multiplying?

• 8 * x - 8 * a

• 7 * x + 7 * a

• 8 * x + 8 * a

• 7 * x - 7 * a

What is the purpose of cross-multiplying in this problem?

• To eliminate fractions

• To divide variables

• To add variables

• To subtract variables

What is the result of distributing 7 on the left side of the equation?

• 8x + 8a

• 7x - 7a

• 8x - 8a

• 7x + 7a

What is the result of distributing 8 on the right side of the equation?

• 7x + 7a

• 8x + 8a

• 8x - 8a

• 7x - 7a

What is the next step after distributing terms on both sides?

• Add 7a to both sides

• Subtract 8x from both sides

• Subtract 7x from both sides

• Add 8a to both sides

After adding 8a to both sides, what is the new equation?

• 7x + 15a = 8x

• 7x + 8a = 15x

• 8x + 15a = 7x

• 15x + 7a = 8x

What is the equation after subtracting 7x from both sides?

• 8a = x

• 15a = 8x

• 7a = x

• 15a = x