Question

hw sec. 2.6
score: 4/8 4/8 answered
question 5
solve for ( a ): ( |2(a + 5)| + 2 = 3 )
( a = )
question help: video ebook

Explanation:

Step1: Isolate the absolute value

Subtract 2 from both sides of the equation \(|2(a + 5)|+2 = 3\) to get \(|2(a + 5)|=3 - 2\), which simplifies to \(|2(a + 5)| = 1\).

Step2: Solve the absolute value equation

The absolute value equation \(|2(a + 5)| = 1\) implies two cases:

• Case 1: \(2(a + 5)=1\)

Divide both sides by 2: \(a + 5=\frac{1}{2}\)
Subtract 5 from both sides: \(a=\frac{1}{2}-5=\frac{1 - 10}{2}=-\frac{9}{2}\)

• Case 2: \(2(a + 5)=- 1\)

Divide both sides by 2: \(a + 5=-\frac{1}{2}\)
Subtract 5 from both sides: \(a=-\frac{1}{2}-5=\frac{-1 - 10}{2}=-\frac{11}{2}\)

Answer:

\(a = -\frac{9}{2}\) or \(a=-\frac{11}{2}\) (or in decimal form \(a=-4.5\) or \(a = - 5.5\))