Question 1

Solve the problem.
-One side of a rectangle is 10 inches and the other side is $x$ inches. Find the value of $x$ if the area must be at least 90 square inches.
A) $x \leq 9$
B) 
C) $x=9$
D) $x \geq 9$

Accepted Answer

The answer of Solve the problem.
-One side of a rectangle...

Question 2

Solve the problem.
-The area of a triangle must be at most 82.5 square inches, the base is 15 inches, and the height is $x$ inches. Find the possible values for $x$.
A) $x<11$
B) 
C)
D)

Accepted Answer

The answer of Solve the problem.
-The area of a triangle...

Question 3

Solve the problem.
-The color guard is making new triangular flags that must have a base of 18 inches to fit on their flagpoles. What is the maximum length of the triangular flags, if they want to use a maximum of 405 in. $^{2}$ of cloth?
A) 45 in.
B) 90 in.
C) 22.5 in.
D) 47 in.

Accepted Answer

The area of a triangle is given by the formula $ \frac{1}{2} \times \text{base} \times \text{height} $. Given a maximum area of 405 square inches and a base of 18 inches, we solve for the height (maximum length of the flag) using the area formula: $ 405 = \frac{1}{2} \times 18 \times \text{height} $. Solving for height gives us 45 inches.

Question 4

Solve the problem.
-A shop keeper is making a triangular sign for his store front, but he must keep the sign under $20 \mathrm{ft}^{2}$ to adhere to zoning laws. If the base of the sign is $20 \mathrm{ft}$, what is the maximum height of the triangular sign?
A) $0.500 \mathrm{ft}$
B) $1.00 \mathrm{ft}$
C) $2.0 \mathrm{ft}$
D) $20 \mathrm{ft}$

Accepted Answer

The area of a triangle is given by the formula $ \frac{1}{2} \times \text{base} \times \text{height} $. To find the maximum height that keeps the area under $20 \mathrm{ft}^{2}$, we set the area to $20 \mathrm{ft}^{2}$ and solve for the height: $20 = \frac{1}{2} \times 20 \times \text{height}$, which simplifies to $20 = 10 \times \text{height}$. Solving for height gives $2.0 \mathrm{ft}$.

Question 5

Provide an appropriate response.
- The solution of the equation $7 y-6=7 y+3$ is zero.

Accepted Answer

The equation $7y - 6 = 7y + 3$ simplifies to $-6 = 3$ when both sides are reduced, indicating no solution exists since the statement is always false, not zero.

Question 6

Provide an appropriate response.
-The solution for the equation $3(6 s-9)=18 \mathrm{~s}-27$ is given as 0 . Is this correct? Explain.

Accepted Answer

The solution is all real numbers. Explanations will vary.

Question 7

Provide an appropriate response.
-Write the steps you would use to solve this equation: $6(x-1)+7 x=-3 x$.

Accepted Answer

The answer of Provide an appropriate response.
-Write the steps you...

Question 8

Provide an appropriate response.
-What value of $K$ makes this equation equivalent to $x=3$ ?
$7 \mathrm{x}-6=\mathrm{K}$

Accepted Answer

The answer of Provide an appropriate response.
-What value of $K$...

Question 9

Provide an appropriate response.
-What value of $K$ makes this equation equivalent to $x=3$ ?
$\frac{9}{K+x}=3$

Accepted Answer

The answer of Provide an appropriate response.
-What value of $K$...

Question 10

Provide an appropriate response.
-What value of $K$ makes this equation equivalent to $x=4$ ?
$6 \mathrm{x}+14 \mathrm{x}-8=\mathrm{K}+5$

Accepted Answer

The answer of Provide an appropriate response.
-What value of $K$...

Question 11

Provide an appropriate response.
-Find all values of $s$ that make this statement true: $6(2 s-8)=12 s-48$.

Accepted Answer

The answer of Provide an appropriate response.
-Find all values of...

Question 12

Provide an appropriate response.
-Find all values of $x$ that make this statement true: $(x-4)+1=(x+1)-4$.

Accepted Answer

The answer of Provide an appropriate response.
-Find all values of...

Quiz 8: Solving Equations and Inequalities

Solve the problem. -One side of a rectangle is 10 inches and the other side is $x$ inches. Find the value of $x$ if the area must be at least 90 square inches.

Solve the problem. -The area of a triangle must be at most 82.5 square inches, the base is 15 inches, and the height is $x$ inches. Find the possible values for $x$ .

Solve the problem. -The color guard is making new triangular flags that must have a base of 18 inches to fit on their flagpoles. What is the maximum length of the triangular flags, if they want to use a maximum of 405 in. $^{2}$ of cloth?

Solve the problem. -A shop keeper is making a triangular sign for his store front, but he must keep the sign under $20 \mathrm{ft}^{2}$ to adhere to zoning laws. If the base of the sign is $20 \mathrm{ft}$ , what is the maximum height of the triangular sign?

Provide an appropriate response. - The solution of the equation $7 y-6=7 y+3$ is zero.

Provide an appropriate response. -The solution for the equation $3(6 s-9)=18 \mathrm{~s}-27$ is given as 0 . Is this correct? Explain.

Provide an appropriate response. -Write the steps you would use to solve this equation: $6(x-1)+7 x=-3 x$ .

Provide an appropriate response. -What value of $K$ makes this equation equivalent to $x=3$ ? $7 \mathrm{x}-6=\mathrm{K}$

Provide an appropriate response. -What value of $K$ makes this equation equivalent to $x=3$ ? $\frac{9}{K+x}=3$

Provide an appropriate response. -What value of $K$ makes this equation equivalent to $x=4$ ? $6 \mathrm{x}+14 \mathrm{x}-8=\mathrm{K}+5$

Provide an appropriate response. -Find all values of $s$ that make this statement true: $6(2 s-8)=12 s-48$ .

Provide an appropriate response. -Find all values of $x$ that make this statement true: $(x-4)+1=(x+1)-4$ .

Quiz 8: Solving Equations and Inequalities

Solve the problem. -One side of a rectangle is 10 inches and the other side is xxx inches. Find the value of xxx if the area must be at least 90 square inches.

Solve the problem. -The area of a triangle must be at most 82.5 square inches, the base is 15 inches, and the height is xxx inches. Find the possible values for xxx .

Solve the problem. -The color guard is making new triangular flags that must have a base of 18 inches to fit on their flagpoles. What is the maximum length of the triangular flags, if they want to use a maximum of 405 in. 2^{2}2 of cloth?

Solve the problem. -A shop keeper is making a triangular sign for his store front, but he must keep the sign under 20ft220 \mathrm{ft}^{2}20ft2 to adhere to zoning laws. If the base of the sign is 20ft20 \mathrm{ft}20ft , what is the maximum height of the triangular sign?

Provide an appropriate response. - The solution of the equation 7y−6=7y+37 y-6=7 y+37y−6=7y+3 is zero.

Provide an appropriate response. -The solution for the equation 3(6s−9)=18 s−273(6 s-9)=18 \mathrm{~s}-273(6s−9)=18 s−27 is given as 0 . Is this correct? Explain.

Provide an appropriate response. -Write the steps you would use to solve this equation: 6(x−1)+7x=−3x6(x-1)+7 x=-3 x6(x−1)+7x=−3x .

Provide an appropriate response. -What value of KKK makes this equation equivalent to x=3x=3x=3 ? 7x−6=K7 \mathrm{x}-6=\mathrm{K}7x−6=K

Provide an appropriate response. -What value of KKK makes this equation equivalent to x=3x=3x=3 ? 9K+x=3\frac{9}{K+x}=3K+x9​=3

Provide an appropriate response. -What value of KKK makes this equation equivalent to x=4x=4x=4 ? 6x+14x−8=K+56 \mathrm{x}+14 \mathrm{x}-8=\mathrm{K}+56x+14x−8=K+5

Provide an appropriate response. -Find all values of sss that make this statement true: 6(2s−8)=12s−486(2 s-8)=12 s-486(2s−8)=12s−48 .

Provide an appropriate response. -Find all values of xxx that make this statement true: (x−4)+1=(x+1)−4(x-4)+1=(x+1)-4(x−4)+1=(x+1)−4 .

Solve the problem. -One side of a rectangle is 10 inches and the other side is $x$ inches. Find the value of $x$ if the area must be at least 90 square inches.

Solve the problem. -The area of a triangle must be at most 82.5 square inches, the base is 15 inches, and the height is $x$ inches. Find the possible values for $x$ .

Solve the problem. -The color guard is making new triangular flags that must have a base of 18 inches to fit on their flagpoles. What is the maximum length of the triangular flags, if they want to use a maximum of 405 in. $^{2}$ of cloth?

Solve the problem. -A shop keeper is making a triangular sign for his store front, but he must keep the sign under $20 \mathrm{ft}^{2}$ to adhere to zoning laws. If the base of the sign is $20 \mathrm{ft}$ , what is the maximum height of the triangular sign?

Provide an appropriate response. - The solution of the equation $7 y-6=7 y+3$ is zero.

Provide an appropriate response. -The solution for the equation $3(6 s-9)=18 \mathrm{~s}-27$ is given as 0 . Is this correct? Explain.

Provide an appropriate response. -Write the steps you would use to solve this equation: $6(x-1)+7 x=-3 x$ .

Provide an appropriate response. -What value of $K$ makes this equation equivalent to $x=3$ ? $7 \mathrm{x}-6=\mathrm{K}$

Provide an appropriate response. -What value of $K$ makes this equation equivalent to $x=3$ ? $\frac{9}{K+x}=3$

Provide an appropriate response. -What value of $K$ makes this equation equivalent to $x=4$ ? $6 \mathrm{x}+14 \mathrm{x}-8=\mathrm{K}+5$

Provide an appropriate response. -Find all values of $s$ that make this statement true: $6(2 s-8)=12 s-48$ .

Provide an appropriate response. -Find all values of $x$ that make this statement true: $(x-4)+1=(x+1)-4$ .