Question

13 mark for review

x + 4

+ 4 =

2x - 11

+ 4

what is the smallest solution to the given equation?

Explanation:

Step1: Simplify the equation

Subtract 4 from both sides of the equation \(|x + 4|+4=|2x - 11|+4\) to get \(|x + 4|=|2x - 11|\).

Step2: Consider cases for absolute values

Case 1: \(x + 4=2x - 11\)
Solve for \(x\):
Subtract \(x\) from both sides: \(4=x - 11\)
Add 11 to both sides: \(x = 15\)

Case 2: \(x + 4=-(2x - 11)\)
Simplify the right - hand side: \(x + 4=-2x + 11\)
Add \(2x\) to both sides: \(3x+4 = 11\)
Subtract 4 from both sides: \(3x=7\)
Divide both sides by 3: \(x=\frac{7}{3}\)

Step3: Compare the solutions

We have two solutions \(x = 15\) and \(x=\frac{7}{3}\). Since \(\frac{7}{3}\approx2.33\) and \(15>\frac{7}{3}\), the smaller solution is \(\frac{7}{3}\).

Answer:

\(\frac{7}{3}\)