6. If $2 x-5< x+4$, which of the following is true?
(A) $x> 9$
B) $2 x< 18$
C) $3 x< 9$
D) $x$ can be all real numbers

Answer

Expert–verified

Hide Steps

Answer

$\boxed{\text{B) } 2x < 18$ is the correct option

Steps

Step 1 ：Solve the inequality: $2x - 5 < x + 4$

Step 2 ：Subtract x from both sides: $x - 5 < 4$

Step 3 ：Add 5 to both sides: $x < 9$

Step 4 ：Check the given options:

Step 5 ：A) $x > 9$ is not true

Step 6 ：B) $2x < 18$ is true for $x < 9$

Step 7 ：C) $3x < 9$ is true for $x < 3$, but not for all $x < 9$

Step 8 ：D) $x$ cannot be all real numbers

Step 9 ：$\boxed{\text{B) } 2x < 18$ is the correct option