How many solutions can be found for the linear equation?
4(x+5)-5 = 8x+18/2
A. no solutions
B. one solution
C. two solutions
D. infinitely many solutions
To find the number of solutions for the linear equation, we need to simplify the equation and see how many variable terms are left.
Starting with the given equation:
4(x + 5) - 5 = 8x + 18/2
First, distribute the 4 on the left side of the equation:
4x + 20 - 5 = 8x + 9
Combine like terms on the left side:
4x + 15 = 8x + 9
Next, subtract 4x from both sides to isolate the variable terms:
15 = 4x + 9 - 8x
Combine like terms on the right side:
15 = -4x + 9
Then, subtract 9 from both sides:
15 - 9 = -4x + 9 - 9
Simplify:
6 = -4x
Finally, divide both sides by -4 to solve for x:
6/-4 = -4x/-4
Simplify:
-3/2 = x
Therefore, there is only one solution for the linear equation.
The correct answer is B. one solution.
To find the number of solutions for the linear equation, we need to simplify and solve for x.
Given equation: 4(x+5)-5 = 8x+18/2
First, let's simplify the equation step by step:
Distribute 4 to both terms inside the parentheses:
4x + 20 - 5 = 8x + 18/2
Combine like terms:
4x + 15 = 8x + 9
Move the variables to one side and constants to the other side:
4x - 8x = 9 - 15
Simplify:
-4x = -6
Divide both sides by -4 to solve for x:
x = -6 / -4
Simplify:
x = 3/2
After solving the equation, we find that there is only one solution for x.
Therefore, the answer is B. one solution.
To determine how many solutions can be found for the given linear equation, we need to simplify and solve it. Let's break it down step by step.
The equation provided is: 4(x+5)-5 = 8x+18/2
First, simplify both sides of the equation:
4(x+5)-5 = 8x+9
Now, distribute the 4 to the terms inside the parentheses:
4x + 20 - 5 = 8x + 9
Next, combine like terms on both sides of the equation:
4x + 15 = 8x + 9
To isolate the variable, subtract 4x from both sides:
15 = 4x + 8x + 9
Combine like terms again:
15 = 12x + 9
Now, subtract 9 from both sides:
15 - 9 = 12x
6 = 12x
Finally, divide both sides by 12:
6/12 = x
1/2 = x
So, the solution to the given equation is x = 1/2.
Since there is only one value for x that satisfies the equation, the answer is:
B. one solution