Question

1. in the given equation \\((k - 4)x = 10\\), \\(k\\) is a constant. if the equation has no solution, what is the value of \\(k\\)?

a. 2
b. 4
c. 6
d. 10

practice 4

1. how many solutions does the equation \\(10(15x - 9) = -15(6 - 10x)\\) have?

a. exactly one
b. exactly two
c. infinitely many
d. zero

1. in the given equation \\(5x + 20 = 5x + k\\), \\(k\\) is a constant. the equation has infinitely many solutions. the value of \\(k\\) is ______.

concept 5: solving literal equations

the equations \\(3x + 4 = 15\\) and \\(6x + 5 = 17\\) have the general form \\(ax + b = c\\).
the equation \\(ax + b = c\\) is called a literal equation because the coefficients and constants have been replaced by letters. when we solve a literal equation, we can use the result to solve any equation that has the same form as the literal equation.

math exploration 5

solve \\(ax + 3 = 12\\) for \\(x\\), where \\(a \
eq 0\\). (use \\(a\\) to represent \\(x\\))

practice 5

solve \\(2x + 3b = 9\\) for \\(x\\). (use \\(b\\) to represent \\(x\\))

exit ticket

1. the solution of \\(x - 1 = 3 - x\\) is ______.

Explanation:

Analyze the first question

$$
LATEXBLOCK0
$$

Analyze the second question

$$
LATEXBLOCK1
$$

Analyze the third question

$$
LATEXBLOCK2
$$

Analyze the fourth question

$$
LATEXBLOCK3
$$

Analyze the fifth question

$$
LATEXBLOCK4
$$

Analyze the sixth question

$$
LATEXBLOCK5
$$

Answer:

Question 1

• A. 2
• B. 4 (Correct answer)
• C. 6
• D. 10

Question 2

• A. Exactly one
• B. Exactly two
• C. Infinitely many (Correct answer)
• D. Zero

Question 3

In the given equation \(5x + 20 = 5x + k\), \(k\) is a constant. The equation has infinitely many solutions. The value of \(k\) is <blank>20</blank>.

Question 4

Solve \(ax + 3 = 12\) for \(x\), where \(a
eq 0\). (Use \(a\) to represent \(x\))
The solution is <blank>\(x = \frac{9}{a}\)</blank>.

Question 5

Solve \(2x + 3b = 9\) for \(x\). (Use \(b\) to represent \(x\))
The solution is <blank>\(x = \frac{9 - 3b}{2}\)</blank>.

Question 6

The solution of \(x - 1 = 3 - x\) is <blank>2</blank>.