Question

Solve 4(x−3)−2(x−1)>0.

a) {x∣x<−5}
b) {x∣x>−5}
c) {x∣x>5}
d) {x,x<5}

Answer 1

To solve the inequality, the distributed terms were simplified to 2x - 10 > 0, and then x > 5 was obtained. The correct solution set for x is all values greater than 5, which matches option (c).

Step-by-step explanation:

The question asks to solve the inequality 4(x−3)−2(x−1)>0. First, we distribute into the parentheses and simplify the inequality:

4x − 12 − 2x + 2 > 0

2x − 10 > 0

Next, we isolate x to solve for the variable:

2x > 10

x > 5

The solution set for the inequality is then all x values greater than 5, which can be expressed as x . Comparing the options presented, the correct choice is (c).