Solve the equation. Graph and check your solutions.
−5|x|=−10
elect the correct choice and, if necessary, fill in the answer box in your choice below.
The given equation is −5|x|=−10
To solve for x, we need to isolate the absolute value expression.
Divide both sides by −5:
|x| = 2
The absolute value of a number is always non-negative (greater than or equal to 0), so we have two cases to consider:
1) x is positive: |x| = x
2) x is negative: |x| = -x
Case 1: x is positive
In this case, the equation becomes:
x = 2
Case 2: x is negative
In this case, the equation becomes:
-x = 2
Multiply both sides by -1 (to get x by itself):
x = -2
Therefore, the solutions for the original equation are x = 2 and x = -2.
To graph and check the solutions, we can plot the points (2, 0) and (-2, 0) on a number line:
---------------
-3 -2 -1 0 1 2 3
-2 2
Both solutions are valid and satisfy the original equation, so the correct choice is: x = 2 and x = -2.
Solve the equation.
10=|m+6|
To solve the equation 10 = |m + 6|, we need to isolate the absolute value expression.
Since the absolute value of a number can never be negative, we can rewrite the equation as:
10 = m + 6 (if m + 6 is positive)
OR
10 = -(m + 6) (if m + 6 is negative)
Case 1: m + 6 is positive
If m + 6 is positive, the equation becomes:
10 = m + 6
Subtract 6 from both sides:
10 - 6 = m
4 = m
So, in this case, the solution is m = 4.
Case 2: m + 6 is negative
If m + 6 is negative, the equation becomes:
10 = -(m + 6)
Remove the negative sign by multiplying both sides by -1:
-10 = m + 6
Subtract 6 from both sides:
-10 - 6 = m
-16 = m
So, in this case, the solution is m = -16.
Therefore, the solutions for the original equation are m = 4 and m = -16.
Solve the equation.
11=|m+7|
To solve the equation 11 = |m + 7|, we need to isolate the absolute value expression.
Since the absolute value of a number can never be negative, we can rewrite the equation as:
11 = m + 7 (if m + 7 is positive)
OR
11 = -(m + 7) (if m + 7 is negative)
Case 1: m + 7 is positive
If m + 7 is positive, the equation becomes:
11 = m + 7
Subtract 7 from both sides:
11 - 7 = m
4 = m
So, in this case, the solution is m = 4.
Case 2: m + 7 is negative
If m + 7 is negative, the equation becomes:
11 = -(m + 7)
Remove the negative sign by multiplying both sides by -1:
-11 = m + 7
Subtract 7 from both sides:
-11 - 7 = m
-18 = m
So, in this case, the solution is m = -18.
Therefore, the solutions for the original equation are m = 4 and m = -18.
To solve the equation -5|x| = -10, you can start by dividing both sides of the equation by -5.
(-5|x|)/-5 = -10/-5
Simplifying this, you have:
|x| = 2
Now, you can solve for the absolute value by considering two cases:
Case 1: |x| = 2
If x is positive, then |x| = x. Therefore, x = 2.
If x is negative, then |x| = -x. Therefore, -x = 2, which gives x = -2.
Therefore, there are two solutions: x = 2 and x = -2.
To graph the equation, you can plot these two solutions on a number line. Mark 2 and -2 on the number line.
To check these solutions, substitute x = 2 and x = -2 back into the original equation:
For x = 2:
-5|2| = -10
-5(2) = -10
-10 = -10
The equation holds true for x = 2.
For x = -2:
-5|-2| = -10
-5(2) = -10
-10 = -10
The equation also holds true for x = -2.
Therefore, the solution to the equation -5|x| = -10 is x = 2 and x = -2.