1.
Solve for x:3x + 5 = 23
Correct Answer
C. 6
Explanation
To solve the equation 3x + 5 = 23, we need to isolate the variable x. First, subtract 5 from both sides of the equation to get 3x = 18. Then, divide both sides of the equation by 3 to solve for x, which gives x = 6. Therefore, the correct answer is 6.
2.
-2x + 8 = -10
Correct Answer
A. 9
Explanation
By solving the given equation, we can find the value of x. To isolate x, we need to get rid of the constant term on the left side of the equation. By subtracting 8 from both sides, we get -2x = -18. To solve for x, we divide both sides by -2, giving us x = 9. Therefore, the correct answer is 9.
3.
21 = 4x - 3
Correct Answer
D. 6
Explanation
To find the value of x in the equation 21 = 4x - 3, we need to isolate the variable x. First, we add 3 to both sides of the equation to get 24 = 4x. Then, we divide both sides by 4 to solve for x, which gives us x = 6. Therefore, the correct answer is 6.
4.
X/2 + 7 = 12
Correct Answer
A. 10
Explanation
To solve the equation x/2 + 7 = 12, we need to isolate x. We can start by subtracting 7 from both sides of the equation. This gives us x/2 = 5. To get rid of the fraction, we can multiply both sides of the equation by 2. This results in x = 10. Therefore, the correct answer is 10.
5.
What is the first step to solving this equation?3x - 8 = 4
Correct Answer
C. Add 8 to each side
Explanation
To solve the equation 3x - 8 = 4, the first step is to add 8 to each side. This is done in order to isolate the variable term, 3x, on one side of the equation. By adding 8 to each side, the equation becomes 3x = 12, allowing for further simplification and solving for x.
6.
120 = -30 - 5x
Correct Answer
D. -30
Explanation
To solve the equation 120 = -30 - 5x, we need to isolate the variable x. We can start by moving the constant term -30 to the other side of the equation by adding 30 to both sides. This gives us 150 = -5x. Then, we divide both sides by -5 to solve for x, resulting in x = -30. Therefore, the correct answer is -30.
7.
What is the second step to solving this equation?x/4 - 6 = -3
Correct Answer
C. Multiply each side by 4
Explanation
To solve the equation x/4 - 6 = -3, the second step is to multiply each side of the equation by 4. This is done to eliminate the fraction x/4 and get rid of the denominator. By multiplying each side by 4, the equation becomes x - 24 = -12, which simplifies the equation further and allows for easier solving.
8.
Tell whether the following solution makes the equation true.10x - 20 = 0 x=2
Correct Answer
A. Yes
Explanation
The given equation is 10x - 20 = 0. To check if the solution x=2 makes the equation true, we substitute x=2 into the equation. Plugging in x=2, we have 10(2) - 20 = 0, which simplifies to 20 - 20 = 0. This equation is true since 0 = 0. Therefore, the solution x=2 makes the equation true.
9.
Tell whether the following solution makes the equation true.
8 + x/5 = 12 x=10
Correct Answer
B. No
Explanation
The given equation is 8 + x/5 = 12. To check if the solution x=10 makes the equation true, we substitute x=10 into the equation.
8 + 10/5 = 12.
8 + 2 = 12.
10 = 12.
Since 10 is not equal to 12, the solution x=10 does not make the equation true. Therefore, the answer is no.
10.
52 = -5x - 3
Correct Answer
A. -11
Explanation
To find the value of x, we need to solve the equation 52 = -5x - 3. We can start by isolating the term with x by adding 3 to both sides of the equation, which gives us 55 = -5x. Then, we can divide both sides by -5 to solve for x. Dividing 55 by -5 gives us x = -11. Therefore, the correct answer is -11.