1. How many solutions can be found for the equation 4x + 5 = 10?
A. Zero
B.One****
C.Two
D.Infinitely Many
2.What is the value of z in the equation
3z − 7 = 14?
A.3
B.4
C.7****
D. 21
They're right!
1. To solve the equation 4x + 5 = 10, we want to isolate the variable x.
First, subtract 5 from both sides of the equation:
4x + 5 - 5 = 10 - 5
4x = 5
Next, divide both sides of the equation by 4 to solve for x:
4x/4 = 5/4
x = 5/4
Therefore, the equation 4x + 5 = 10 has one solution, which is x = 5/4.
2. To solve the equation 3z - 7 = 14, we want to isolate the variable z.
First, add 7 to both sides of the equation:
3z - 7 + 7 = 14 + 7
3z = 21
Next, divide both sides of the equation by 3 to solve for z:
3z/3 = 21/3
z = 7
Therefore, the value of z in the equation 3z - 7 = 14 is z = 7.
To find the number of solutions for an equation, you need to solve the equation and determine how many distinct values satisfy the equation.
1. For the equation 4x + 5 = 10, you can solve it as follows:
Subtract 5 from both sides of the equation:
4x + 5 - 5 = 10 - 5
4x = 5
Divide both sides of the equation by 4:
(4x) / 4 = 5 / 4
x = 5/4
The equation has only one solution, which is x = 5/4. The correct answer is B. One.
2. For the equation 3z - 7 = 14, you can solve it as follows:
Add 7 to both sides of the equation:
3z - 7 + 7 = 14 + 7
3z = 21
Divide both sides of the equation by 3:
(3z) / 3 = 21 / 3
z = 7
The equation has only one solution, which is z = 7. The correct answer is C. 7.
For question 2, the answer is 7
7=z