Solve the inequality and express the solution set using interval notation. $0.1 x + 0.05 ( x + 400 ) 38$
A) $( - \infty , 120 )$
B) $( 120 , \infty )$
C) $( - \infty , 120 ]$
D) $[ 120 , \infty )$
E) $[ 120 , \infty ]$

Question

Solve the inequality and express the solution set using interval notation. $0.1 x + 0.05 ( x + 400 ) > 38$
A) $( - \infty , 120 )$
B) $( 120 , \infty )$
C) $( - \infty , 120 ]$
D) $[ 120 , \infty )$
E) $[ 120 , \infty ]$

Quizplus · Accepted Answer

First, simplify the inequality: $0.1x + 0.05(x + 400) > 38$. Distribute the 0.05: $0.1x + 0.05x + 20 > 38$. Combine like terms: $0.15x + 20 > 38$. Subtract 20 from both sides: $0.15x > 18$. Divide by 0.15: $x > 120$. This means the solution is all values greater than 120, which is represented by the interval notation $(120, \infty)$.

Solve the Inequality and Express the Solution Set Using Interval 0.1x+0.05(x+400)>380.1 x + 0.05 ( x + 400 ) > 380.1x+0.05(x+400)>38

Solve the Inequality and Express the Solution Set Using Interval $0.1 x + 0.05 ( x + 400 ) > 38$