Questions: Solve: (1/2)x+3+2 ≤ 5

Solve: (1/2)x+3+2 ≤ 5
Transcript text: Solve: $\frac{1}{2}|x+3|+2 \leq 5$
failed

Solution

failed
failed

Solution Steps

To solve the inequality \(\frac{1}{2}|x+3|+2 \leq 5\), we can follow these steps:

  1. Isolate the absolute value expression by subtracting 2 from both sides.
  2. Multiply both sides by 2 to eliminate the fraction.
  3. Solve the resulting absolute value inequality by considering both the positive and negative scenarios.
Step 1: Isolate the Absolute Value Expression

Start with the inequality: \[ \frac{1}{2}|x+3| + 2 \leq 5 \] Subtract 2 from both sides: \[ \frac{1}{2}|x+3| \leq 3 \]

Step 2: Eliminate the Fraction

Multiply both sides by 2: \[ |x+3| \leq 6 \]

Step 3: Solve the Absolute Value Inequality

The inequality \(|x+3| \leq 6\) can be split into two separate inequalities: \[ -6 \leq x+3 \leq 6 \] Subtract 3 from all parts: \[ -9 \leq x \leq 3 \]

Final Answer

\(\boxed{-9 \leq x \leq 3}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Solve the following system of linear equations by graphing: -5/3 x + 1/2 y = 7/5 -20/3 x + 2 y = 1
failedAnswered
Write the expression as a sum, difference, or product of simpler logarithms. log6(5k) = □
failedAnswered
Question 2 1 pts Mexican chemist Mario J. Molina was one of three chemists who received the Nobel Prize in chemistry in 1995 for his work in determining that chloroflourocarbons (CFCs) release Cl atoms into the atmosphere, leading to the depletion of the ozone layer. The two-step mechanism for the resulting reaction is shown below. step 1 Cl+O3 -> ClO+O2 step 2 ClO+O -> Cl+O2 Why does a small amount of CFCs lead to a large loss of ozone? (There may be more than one answer. Select all that apply.) Since it is a catalyst, it must absorb UV radiation from sunlight before it can be active. As a catalyst, it is created in the reaction mixture before it changes the rate of the reaction As a catalyst, it can speed up many cycles of the same reaction Because it is a catalyst, it causes the reaction to occur faster but isn't consumed during the reaction. Since it is a catalyst, it stabilizes the products of the reaction
failedAnswered
The rate constant of a certain reaction is known to obey the Arrhenius equation, and to have an activation energy Eα=67.0 kJ / mol. If the rate constant of this reaction is 7.6 M^-1 s^-1 at 158.0°C, what will the rate constant be at 201.0°C? Round your answer to 2 significant digits.
failedAnswered
What is the final step in the scientific method? Making a conclusion and recommendation Analyzing results Collecting data Designing an experiment