Solve and graph the equation.
l x l = 9
To solve the equation l x l = 9, we need to find the value of l that satisfies the equation.
Taking the square root of both sides of the equation, we have:
|l| = √9
Since the square root of 9 is 3, we have:
|l| = 3
This equation can be rewritten as two separate equations:
l = 3 or l = -3
Therefore, the equation has two potential solutions, l = 3 or l = -3.
To graph the equation, we plot the two solutions on a number line:
-3 3
The graph would have a solid dot at the point -3 and a solid dot at the point 3. The line connecting the two dots would be included (solid line) because the equation includes the absolute value function.
To solve the equation |x| = 9, we need to consider two cases:
Case 1: x is positive:
If x is positive, then the equation |x| = 9 simplifies to x = 9. So in this case, the solution is x = 9.
Case 2: x is negative:
If x is negative, then |x| will be positive and |x| = 9 simplifies to -x = 9. To solve for x in this case, we need to multiply both sides of the equation by -1 and flip the sign, resulting in x = -9.
Hence, the solution to the equation |x| = 9 is x = 9 and x = -9.
To graph this equation, we can plot the points on a number line. Place a point labeled 9 to the right of the origin and another point labeled -9 to the left of the origin. Then draw a solid line connecting the two points to show that all values between -9 and 9 satisfy the equation.
To solve the equation |x| = 9, we need to find the values of x that satisfy it. We can solve this equation by considering two cases: when x is positive and when x is negative.
Case 1: x is positive
If x is positive, then |x| = x. So the equation simplifies to x = 9. The value of x that satisfies this equation is x = 9.
Case 2: x is negative
If x is negative, then |x| = -x. So the equation simplifies to -x = 9. We can solve this equation by multiplying both sides by -1, giving us x = -9.
Therefore, the two solutions to the equation |x| = 9 are x = 9 and x = -9.
To graph this equation, we can plot the two solutions on a number line. Place a filled-in circle at 9 and a filled-in circle at -9. Then draw a solid line connecting the two points. This represents all the values of x that satisfy the equation.