Extra Practice In Exercises 1-6, solve the literal equation for y.

The Correct Answer and Explanation is:

Of course. Here are the correct answers for the visible math problems, followed by an explanation of the methods used to solve them.

Correct Answers

Exercises 1–6: Solve for y

1. y = 2x + 15
2. y = 2 – 4x
3. y = x – 2
4. y = 11 – x
5. y = 3x + 4
6. y = (3x – 6) / -4 or y = (6 – 3x) / 4

Exercises 7–12: Solve for x
7. x = y / 6
8. x = q / (3 + 9z)
9. x = (r – 4) / (7 – s)
10. x = (y + 6) / 6
11. x = (4g – r) / -2 or x = (r – 4g) / 2
12. x = (4z – 4) / 3

Explanation

Solving a literal equation means isolating one specific variable in an equation that contains multiple variables. The process uses the same fundamental principles as solving a standard one-variable equation. The goal is to perform inverse operations to move all other terms to the opposite side of the equal sign, leaving the desired variable by itself.

For the first set of exercises, the goal was to solve for y. In problems like number 1 (y – 2x = 15), you isolate y by performing the opposite operation. Since 2x is being subtracted from y, you add 2x to both sides, resulting in y = 2x + 15. For problem 5 (3x – y = -4), you first subtract 3x from both sides to get -y = -4 – 3x. Because the y is negative, you must then multiply or divide the entire equation by -1 to find the value of positive y, which gives you y = 4 + 3x.

The second set of exercises required solving for x. These problems introduce a key step for when the variable appears in multiple terms. In problem 7 (y = 10x – 4x), you must first combine the like terms on the right side to get y = 6x before dividing by 6. For a problem like number 8 (q = 3x + 9xz), you cannot simply combine the terms. Instead, you must factor the x out of both terms, which gives you q = x(3 + 9z). From there, you can isolate x by dividing both sides by the entire expression in the parentheses. This factoring technique is essential for isolating a variable that is present in multiple, unlike terms. The final answer is an expression containing other variables, not a single number.thumb_upthumb_down