1. 1.01 Rearranging Linear Inequalities
Unit: Optimization

2. To isolate the y-variable Function Form: 𝒚= 𝒂𝒙+𝒃
Goal
To isolate the y-variable Function Form: 𝒚= 𝒂𝒙+𝒃

3. How To:
Goal is to get the y term on one side of the inequality, and everything else on the other side. To do this:
Use algebra to bring the term with the y-variable to the left side of the inequality (if it isn’t already there), the same way you would if there was an =
Bring all other terms to the right side of the inequality, the same way you would if there was an =
Divide everything by the coefficient of y If the coefficient is negative, the inequality symbol FLIPS (ex: from < to >).

4. 2𝑥+3𝑦−9<0 3𝑦<−2𝑥+9 3𝑦 3 < −2𝑥+9 3 𝑦<− 2 3 𝑥+3
Bring the term with the y-variable to the left side of equation
Bring any other terms to the right side of the equation
Divide everything by the coefficient of y (If the coefficient is negative, the inequality symbol FLIPS)
3𝑦<−2𝑥+9
3𝑦 3 < −2𝑥+9 3
𝑦<− 2 3 𝑥+3

5. 5𝑥−2𝑦+13≤0 −2𝑦≤−5𝑥−13 −2𝑦 −2 ≤ −5𝑥−13 −2 𝑦≥ 5 2 𝑥+ 13 2
Bring the term with the y-variable to the left side of equation
Bring any other terms to the right side of the equation
Divide everything by the coefficient of y (If the coefficient is negative, the inequality symbol FLIPS)
−2𝑦≤−5𝑥−13
−2𝑦 −2 ≤ −5𝑥−13 −2
𝑦≥ 5 2 𝑥+ 13 2

6. 7−2𝑥>3𝑦 7−2𝑥−3𝑦>0 −3𝑦>2𝑥−7 −3𝑦 −3 > 2𝑥−7 −3
Bring the term with the y-variable to the left side of equation
Bring any other terms to the right side of the equation
Divide everything by the coefficient of y (If the coefficient is negative, the inequality symbol FLIPS)
7−2𝑥−3𝑦>0
−3𝑦>2𝑥−7
−3𝑦 −3 > 2𝑥−7 −3
𝑦<− 2 3 𝑥+ 7 3

7. 3𝑥 2 − 4𝑦 5 >1
Bring the term with the y-variable to the left side of equation
Bring any other terms to the right side of the equation
Divide everything by the coefficient of y (If the coefficient is negative, the inequality symbol FLIPS)
− 4𝑦 5 >− 3𝑥 2 +1
− 4𝑦 5 − 4 5 > − 3𝑥 2 +1 − 4 5
𝑦< 15 8 𝑥− 5 4