Solve $\frac{|2 x+2|}{5}=-3$
Answer (2)
Multiply both sides of the equation by 5: ∣2 x + 2∣ = − 15 .
Since the absolute value cannot be negative, there are no solutions.
The equation has no solution. No solutions
Explanation
Understanding the Problem We are given the equation 5 ∣2 x + 2∣ = − 3 and we need to find the value(s) of x that satisfy this equation.
Isolating the Absolute Value First, let's isolate the absolute value term by multiplying both sides of the equation by 5:
Examples
Absolute value equations can be used to model real-world situations where distance from a reference point is important, such as in manufacturing where parts must be within a certain tolerance of a specified measurement. For example, if a machine is set to produce rods that are 10 cm long, and the acceptable tolerance is 0.1 cm, the length x of the rods produced must satisfy the equation ∣ x − 10∣ ≤ 0.1 . This ensures that the rods are not too far from the desired length.
The equation 5 ∣2 x + 2∣ = − 3 has no solutions because absolute values cannot be negative. Thus, the final answer is that there are no solutions. No solutions
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