How many solutions can be found for the linear equation?
4(x + 5) - 5 = 8x+182
Responses
A no solutionsno solutions
B one solutionone solution
C two solutionstwo solutions
D infinitely many solutions
A: no solutions
To determine the number of solutions for the linear equation, we need to simplify the equation and solve for x.
Step 1: Distribute the 4 to terms inside the parentheses:
4x + 20 - 5 = 8x + 182
Step 2: Combine like terms on both sides of the equation:
4x + 15 = 8x + 182
Step 3: Subtract 4x from both sides:
15 = 4x + 182
Step 4: Subtract 182 from both sides:
-167 = 4x
Step 5: Divide both sides by 4:
-167/4 = x
The solution to the equation is x = -167/4.
Since there is only one solution, the answer is option B: one solution.
To determine how many solutions can be found for the linear equation, we first need to simplify the equation and solve for the variable x.
Let's simplify the given equation step by step:
4(x + 5) - 5 = 8x + 182
First, distribute 4 to both terms inside the parentheses:
4x + 20 - 5 = 8x + 182
Simplify further by combining like terms:
4x + 15 = 8x + 182
Now, let's isolate the variable x by moving all the terms with x to one side and the constant terms to the other side:
4x - 8x = 182 - 15
-4x = 167
Divide both sides of the equation by -4 to solve for x:
x = 167 / (-4)
x = -41.75
Since we have found a numerical value for x, we can conclude that there is only one solution to the linear equation.
Therefore, the answer is B - one solution.