EXAMPLE 3 Solve the compound inequality. Graph the solution set and write it usi

Question

EXAMPLE 3 Solve the compound inequality. Graph the solution set and write it using Merol set-builder notation. x+3s 2x-1 and 3x 2 1 is shown below in blue. r> 1 x24 Only those values of x where x 2 4 and x > 1 are in the solution set of the compound inequality. nce all numbers greater than or equal to 4 are also greater than 1, the solutions are the numbers x where x 2 4. The solution set is the interval whose graph is shown below. Written using set-builder notation, the solution set is (x I x 2 4) Page 2 of B Self Check 3 Solve the compound inequality 3x +5

Explanation / Answer

Solution: We will solve the given compound inequality separately.

So, lets first solve 3x+5<6x+1 and then we will solve next inequality 3x+2<6x+2

So solving with the first inequality i.e. 3x+5<6x+1

3x+5-1<6x+1-1 (Add (-1) on both sides)

3x+4<6x

3x+4-3x<6x-3x (Add (-3x) on both sides)

4<3x or x>4/3.................................................................(i)

Now solving the next inequality i.e.3x+2<6x+2

3x+2-2 <6x+2 -2 (Add (-2) on both sides)

3x<6x

3x-3x<6x-3x (Add (-3x) on both sides)

0<3x or x>0..........................................(ii)

So, from (i) and (ii) , we can x>4/3 and x>0

So, only those values where x>4/3 and x>0 are in the solution set of ithis compound inequality and is written as {x|x>4/3}.

Clearly if x>4/3 that means x will be > 0, so the best possible graph for this given compound inequality is option (D)

The interval notation for this inequality is [0,?)U[4/3,?)  

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