Sure! Let's solve the given inequality step-by-step.
The inequality we need to solve is:
[tex]\[ 5x - 10 \leq 20 \][/tex]
Step 1: Isolate the term with [tex]\( x \)[/tex].
First, add 10 to both sides of the inequality to eliminate the constant term on the left side:
[tex]\[ 5x - 10 + 10 \leq 20 + 10 \][/tex]
This simplifies to:
[tex]\[ 5x \leq 30 \][/tex]
Step 2: Solve for [tex]\( x \)[/tex].
Now, divide both sides by 5 to isolate [tex]\( x \)[/tex]:
[tex]\[ \frac{5x}{5} \leq \frac{30}{5} \][/tex]
This simplifies to:
[tex]\[ x \leq 6 \][/tex]
Therefore, the solution to the inequality [tex]\( 5x - 10 \leq 20 \)[/tex] is:
[tex]\[ x \leq 6 \][/tex]
Step 3: Express the solution in interval notation.
The inequality [tex]\( x \leq 6 \)[/tex] corresponds to all values of [tex]\( x \)[/tex] that are less than or equal to 6. In interval notation, this is written as:
[tex]\[ (-\infty, 6] \][/tex]
So, the correct interval notation for the solution is:
[tex]\[ (-\infty, 6] \][/tex]
Among the given options, the correct choice is:
[tex]\[ (-\infty, 6] \][/tex]
