Question
Solve absolute value equation :
The correct answer is: no value of x satisfies the given equation.
Hint:
|x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by
So, we will get two cases in the solution of the given equation. We simplify the equation as much as possible and then apply the above definition to get the value of x.
Step by step solution:
The given equation is
|x| + 4 = -9
Subtracting 4 from both sides, we get
|x| = -4 - 9
Simplifying the above equation, we can write
|x| = -13
But |x| is always a non-negative value.
Hence, it can never be equal to -13, which is a negative value.
Thus, no value of x satisfies the given equation.
Note:
Absolute value of a variable has many uses in mathematics. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘ mod x’.
Related Questions to study
Solve absolute value equation :
Solve absolute value equation :
Write an expression for each product without perfect square factors in the radicand. 2√12x9 × √18x5
Write an expression for each product without perfect square factors in the radicand. 2√12x9 × √18x5
Solve absolute value equation :
Solve absolute value equation :
A bee files at 20 feet per second directly to an orange groove from its hive. The bee stays at the orange groove for 15 min , then files directly back to the hive at 12 feet per second. It is away from the hive for a total of 20 mins.
a) What equation can you use to find the distance of the orange grove from the hive ?
b) How far is the orange grove from the hive ?
A bee files at 20 feet per second directly to an orange groove from its hive. The bee stays at the orange groove for 15 min , then files directly back to the hive at 12 feet per second. It is away from the hive for a total of 20 mins.
a) What equation can you use to find the distance of the orange grove from the hive ?
b) How far is the orange grove from the hive ?
Solve absolute value equation :
Solve absolute value equation :
Solve each absolute value inequality. Graph the solution
Solve each absolute value inequality. Graph the solution
Solve - 0.85t - 0.85t -3.9 = - 8.15
An equation in which highest power of any variable is always 1 is known as a Linear equation.
We will simplify the given equation and find the value of t.
Solve - 0.85t - 0.85t -3.9 = - 8.15
An equation in which highest power of any variable is always 1 is known as a Linear equation.
We will simplify the given equation and find the value of t.
Solve 1.037x + 0.02X + 25 = 30.285
An equation in which highest power of any variable is always 1 is known as a Linear equation.
We will simplify the given equation and find the value of x.
Solve 1.037x + 0.02X + 25 = 30.285
An equation in which highest power of any variable is always 1 is known as a Linear equation.
We will simplify the given equation and find the value of x.