Set both inequalities greater than or less than zero. Transform the second inequality so both have the same inequality symbol. Apply the Transitive Property and solve. Make sure the leading coefficient is positive. x-7>5 and 1-4y<6

x-7>5→

1-4y<6→

Combined inequality

a. 0>4y+7

b. X+2>0

c. X+4y>7

d. x-12>0

e. 0>(-4y-5)

f. X-4y>5

Isolate x. Isolate y. Subtract 5 from both sides of the first inequality and 7 from both sides of the second inequality. Solve for x and

1-4y<6→

Combined inequality

a. 0>4y+7

b. X+2>0

c. X+4y>7

d. x-12>0

e. 0>(-4y-5)

f. X-4y>5

f. c. X+4y>7

To solve for x-7>5, apply the Transitive Property to reach 1-4y<6 which states that -1-16y<2 or 4y>2 or X+4y>7. Therefore c is the correct answer choice.

To solve for 1-4y<6, apply the Transitive Property to reach x-7>5 which states that X+2>0. Solve this equation to reach X+4y>7. Therefore f is the correct answer choice.

a. 0>4y+7→

b. X+2>0→

c. X+4y>7→

d. x-12>0→

e. 0>(-4y-5)→

f. X-4y>5 →

g. -3x+10<0 →

h. (x+3) (x-4) > 0 →

a. 0>4y+7→ 4y>7 → y>0

b. X+2>0→ -2>X → X<-10

c. X+4y>7→ X+4 (X) > 7 → X>3

d. x-12>0→ -12 >x → x<-1

e. 0>(-4y-5)→ -4y-5 <0 → y>5

f. X-4y>5 → X+4 (X) > 5 → X > -1

g. -3x+10<0 → -3x-30 <0→ x>30

h. (x+3) (x-4) > 0 → x(x-4) >0 → x≠ -4, X≠4, X≠-3, x ≠ 9, x ≠-12 or (x≠ 3, x≠ -1) and (X≠ 4, X≠ -3)

3. b

4. d

5. f

6. h

7. a

8. e

9 c 10 g 11 i 12 b

13 j 14 h 15 k

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