Solving Linear Equations Quiz

Explanation
The correct answer is "both sides have the same value" because the equal sign in an equation is used to show that the value on the left side of the equation is equal to the value on the right side. It indicates that both sides of the equation represent the same quantity or value.

Explanation
An expression is a mathematical or logical statement that does not involve an equal sign. It represents a value or a computation but does not state that two things are equal. Therefore, the given statement is true.

Explanation
The correct answer is "creates balance". Solving an equation involves finding a value that creates balance between the two sides of the equation. This means that when the value is substituted into the equation, both sides are equal. By finding this value, we can determine the unknown variable in the equation.

Explanation
To find the value of a, we need to isolate it on one side of the equation. First, we subtract 3 from both sides of the equation: 4a + 3 - 3 = 23 - 3. This simplifies to 4a = 20. Next, we divide both sides of the equation by 4 to solve for a: 4a/4 = 20/4. This simplifies to a = 5. Therefore, the value of a is 5.

Explanation
The equation 21 = 7q can be solved by dividing both sides of the equation by 7. This will give us q = 3.

Explanation
The equation 45/r = 5 can be solved by multiplying both sides of the equation by r to isolate r on one side. This gives us 45 = 5r. To solve for r, we divide both sides of the equation by 5, resulting in r = 9.

Explanation
The equation 3(4 + e) = 33 can be solved by first simplifying the expression inside the parentheses. Adding 4 to e gives us 4 + e. Multiplying this by 3 gives us 3(4 + e) = 3(4 + e) = 12 + 3e. Setting this equal to 33, we have 12 + 3e = 33. Subtracting 12 from both sides gives us 3e = 21. Dividing both sides by 3 gives us e = 7. Therefore, the correct answer is 7.

Explanation
By distributing the 6 to both terms inside the parentheses, we get 6w - 12 = 6. Then, by adding 12 to both sides of the equation, we get 6w = 18. Finally, dividing both sides by 6, we find that w = 3.

Explanation
To solve the equation, we need to isolate the variable q. First, we distribute the 7 to the terms inside the parentheses: 21q + 56 = 14. Then, we subtract 56 from both sides to get 21q = -42. Finally, we divide both sides by 21 to solve for q, which gives us q = -2. Therefore, the correct answer is -2.

Explanation
The equation given is 5e + 3 = 33. To solve for e, we need to isolate the variable e. Subtracting 3 from both sides of the equation, we get 5e = 30. Dividing both sides of the equation by 5, we find that e = 6.

Explanation
The given equation can be solved by multiplying both sides of the equation by 3 to eliminate the denominator. This gives us 2a - 5 = 9. Adding 5 to both sides of the equation, we get 2a = 14. Finally, dividing both sides of the equation by 2, we find that a = 7.

Explanation
To solve the equation, we can start by multiplying both sides of the equation by 5 to eliminate the fraction. This gives us 7(2a + 3) = -35. Next, we can distribute the 7 on the left side of the equation, resulting in 14a + 21 = -35. To isolate the variable, we can subtract 21 from both sides, giving us 14a = -56. Finally, dividing both sides by 14, we find that a = -4. Therefore, the correct answer is -4.

Explanation
To solve for the value of q in the equation:
5(2 - 3q)/4(3 + 4q) = -50
Follow these steps:
First, simplify both sides of the equation by multiplying both sides by the denominators to clear the fractions. Multiply both sides by 4(3 + 4q) to eliminate the fraction on the right side:
5(2 - 3q) = -50 * 4(3 + 4q)
Distribute the values on both sides:
10 - 15q = -200(3 + 4q)
Now, distribute -200 on the right side of the equation:
10 - 15q = -600 - 800q
Move the terms involving q to one side of the equation and constants to the other side:
-15q + 800q = -600 - 10
Combine like terms:
785q = -610
Finally, isolate q by dividing both sides by 785:
q = -610 / 785
Now, you can simplify or approximate this fraction as needed:
q ≈ -0.775
So, the value of q is approximately -0.775.