Solve the equation. Graph and check your solutions. - 4|x| = - 20 Select the correct choice and, if necessary, fill in the answer box in your choice below.
OA. x = (Simplify your answer. Use a comma to separate answers as needed.)
OB. There is no solution.
To solve the equation - 4|x| = - 20, we will begin by isolating the absolute value expression.
Dividing both sides of the equation by -4, we get:
|x| = 5
Next, we can split the absolute value equation into two separate equations, one positive and one negative.
For the positive case:
x = 5
For the negative case:
-x = 5
Multiplying by -1 on both sides of the equation, we get:
x = -5
So we have two solutions: x = 5 and x = -5.
To graph these solutions, we can plot the two points (5, 0) and (-5, 0) on a number line.
Checking the solutions back into the original equation:
For x = 5:
-4(5) = -20
-20 = -20 (True)
For x = -5:
-4(-5) = -20
20 = -20 (False)
The only solution that satisfies the original equation is x = 5.
Therefore, the correct choice is:
OA. x = 5
To solve the equation -4|x| = -20, we first need to isolate the absolute value expression.
Dividing both sides of the equation by -4, we get:
|x| = (-20) / (-4)
Simplifying the right side:
|x| = 5
The absolute value of any number is always non-negative. Therefore, for |x| to equal 5, x must be either 5 or -5.
So, the solution to the equation is:
x = 5, -5
To graphically check our solutions, we can plot the equation -4|x| = -20 on a coordinate plane:
The graph of -4|x| = -20 will be a downward-opening V-shape passing through the points (5, -20) and (-5, -20).
To solve the equation -4|x| = -20:
Step 1: Separate the equation into two cases:
Case 1: x is positive (x ≥ 0)
In this case, the absolute value of x is just x. So the equation becomes -4x = -20.
Case 2: x is negative (x < 0)
In this case, the absolute value of x is -x. So the equation becomes -4(-x) = -20, which simplifies to 4x = -20.
Step 2: Solve each case separately:
Case 1: -4x = -20
Divide both sides of the equation by -4:
-4x / -4 = -20 / -4
x = 5
Case 2: 4x = -20
Divide both sides of the equation by 4:
4x / 4 = -20 / 4
x = -5
Step 3: Check the solutions:
To graph the equation, plot the solutions on a number line:
x = 5 (Case 1)
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
x = -5 (Case 2)
○ ●
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-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
Both solutions, x = 5 and x = -5, satisfy the equation -4|x| = -20. Therefore, the correct answer is OA. x = 5,-5.