Solving Algebra Problem: Write two Separate Inequalities (Coursework Sample)

Algebra
Name
Institution
Algebra
1 -12 < 12 + 4x < 0
First step: write as two separate inequalities
-12 < 12 + 4x and12 + 4x > 0
Step two: solve both inequalities separately for the value of x
-12 < 12 + 4x12 + 4x > 0
-12 -12 < 4x 4x > -12
-24 < 4x4x/4> -12/4
-24/4 <4x/4x > -3
-4
The compound inequality can be interpreted as
-4 -3
This can be rewritten as set notation showing intersection of sets
{x: -4 < x > -3 }
This is an intersection of intervals (-4, -3). This means that all the values between -4 and -3 are solutions to the compound inequality (Aufmann & Lockwood, 2013).
The graph on the number line will be:
4857753695700038957252286000041910035242500270510024638000321945023876000351472523749000center2749550022860002768600018186402749550013430252863850094297528638500504190264795004762504000500087630035052000
-4 -3 -2 -1 0 1 2 3 4
All values within the thick line on the number line would solve the compound inequality.
2 12 – x > 15 or 7x – 13 > 1
First step is to solve both the inequalities separately
12- x > 157x – 13 > 1
-x > 15 – 127x > 1 + 13
-x > 37x > 14
-x/- 1> 3/-17x/7 > 14/7
x < - 3x > 2
Division of the inequality by a negative number leads to change of the inequality sign (Hansen, 2014). Hence, > changed to < when divided by - 1
The compound inequality can be interpreted as
x < - 3 or x > 2
The set notation will be { x: x < -3 or x > 2 } showing union of sets.
The values of x less than – 3 satisfy the inequality or values of x le...