Question

a compound inequality is when there are two separate inequalities connected by the word\ ______ \or\ or\. (fill in the blank with the most specific word that makes the statement true.)
question 2
2 points
which is a possible solution for the compound inequality? ( 3x - 5 > 10 ) or ( 2x + 3 leq -7 )
( circ -5 )
( circ 0 )
( circ 5 )
( circ -2 )
question 3
2 points
solve the inequality ( 4x - 3 > 5 ) and ( 2x + 7 < 15 ).
(fill in each blank with an integer or an inequality symbol)
____ __ ( geq ) __ ____

Explanation:

Step1: Fill compound inequality blank

Compound inequalities use "and" or "or" to connect two inequalities; the specific missing word here is "and".

Step2: Solve first compound inequality

Substep2a: Solve $3x - 5 > 10$

Add 5 to both sides: $3x > 15$
Divide by 3: $x > 5$

Substep2b: Solve $2x + 3 \leq -7$

Subtract 3 from both sides: $2x \leq -10$
Divide by 2: $x \leq -5$

Substep2c: Match to options

The solution set is $x > 5$ or $x \leq -5$. Only -5 fits this set.

Step3: Solve second compound inequality

Substep3a: Solve $4x - 3 > 5$

Add 3 to both sides: $4x > 8$
Divide by 4: $x > 2$

Substep3b: Solve $2x + 7 < 15$

Subtract 7 from both sides: $2x < 8$
Divide by 2: $x < 4$

Substep3c: Combine solutions

The combined solution is $2 < x < 4$.

Answer:

1. and
2. A. -5
3. $2$ $<$ $x$ $<$ $4$