Solve the linear equation/inequality. for inequality leave the answer in interval notation.

Question

1.Solve the linear equation/inequality. for inequality leave the answer in  interval notation.

i. 11-3x/4 greater then equal to 5

 

ii 5-x+2/3=7

 

2. 3x+1/4+x+2/3>5-x/2

 

3. 2x-5/7 less then equal to 5

Answer 1

1. 11 - 3x/4 ≥ 5, 

        -3x/4 ≥ -6                      Subtract 11 from both sides

            x   ≤ (-6)(-4/3)           Multiply both sides by (-4/3)

            x   ≤ 8

     The solution, in interval form, is ( -∞, 8].

 

5-x + 2/3 = 7

5-x= 6 1/3           Subtract (2/3) from both sides

-x = 1 1/3            Subtract 5 from both sides

 x = -1 1/3            Multiply both sides by (-1)

 

3x+ 1/4 + x + 2/3   >   5 - x/2

           4x + 11/12   >   5 - x/2         simplify

               4x + x/2   >   5 - 11/12     Collect like terms

                    9/2 x  > 49/12             Simplify

                           x > 49/54             Multiply both sides by (2/9)

The solution, in interval form, is ( 49/54, ∞).

 

2x - 5/7≤ 5

      2x  ≤ 5 + 5/7.            Add 5/7 to both sides

        x  ≤ (40/7)(1/2)        Multiply both sides by(1/2)

        x ≤ 20/7

The solution, in interval form, is (- ∞, 20/7].