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
Elemental sulfur exists in two crystalline forms, rhombic and monoclinic. From the following data, calculate the equilibrium temperature at which monoclinic sulfur and rhombic sulfur are in equilibrium. - Delta Hf°(kJ / mol) and S°(J / K mol): S (rhombic): 0, 31.880 S (monoclinic): 0.30, 32.546 450 K 200 K -200 K -450 K 0 K
failedAnswered
In North America, which anthropogenic biome is most closely associated with areas of stable terrain? Wildlands Remote rangelands Populated croplands Residential rangelands Remote croplands
failedAnswered
Select your answer (13 out of 14) At a rehearsal dinner the night before a wedding, the bride and groom need to assign 10 people to two tables of five people. How many different seating arrangements are there?
failedAnswered
Find the variation constant and an equation of variation where y varies directly as x and y=5 when x=32. The variation constant is 5/32 (Type an integer or a fraction.) The equation of variation is y=5.
failedAnswered
Your textbook suggests that to compose an ethically good and persuasive public speech you should avoid risk. (A) True (B) False