Let's solve the inequality step-by-step.
The given inequality is:
[tex]\[ 58 - 10x \leq 20 + 9x \][/tex]
First, we want to isolate the variable [tex]\( x \)[/tex]. To do this, we'll move all terms involving [tex]\( x \)[/tex] to one side of the inequality and constants to the other side.
1. Subtract [tex]\( 20 \)[/tex] from both sides:
[tex]\[ 58 - 20 - 10x \leq 9x \][/tex]
[tex]\[ 38 - 10x \leq 9x \][/tex]
2. Add [tex]\( 10x \)[/tex] to both sides to get all [tex]\( x \)[/tex]-terms on one side:
[tex]\[ 38 \leq 19x \][/tex]
3. Divide both sides by [tex]\( 19 \)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{38}{19} \leq x \][/tex]
[tex]\[ 2 \leq x \][/tex]
This can also be written as:
[tex]\[ x \geq 2 \][/tex]
So, the solution to the inequality [tex]\( 58 - 10x \leq 20 + 9x \)[/tex] is [tex]\( x \geq 2 \)[/tex].
The correct answer choice is:
D. [tex]\( x \geq 2 \)[/tex]
This means the values of [tex]\( x \)[/tex] that satisfy the inequality are all numbers greater than or equal to 2.
