Answer:
The solutions of [tex]5x-10\le \:20[/tex] are [tex](-\infty \:,\:6][/tex], so C is the correct answer.
Step-by-step explanation:
The expression [tex]5x-10\le \:20[/tex] is an inequality. An inequality is a mathematical statement that compares two expressions using an inequality sign.
The important thing about inequalities is that there can be multiple solutions.
To find all the solutions of [tex]5x-10\le \:20[/tex] you must:
[tex]\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\5x-10+10\le \:20+10[/tex]
[tex]\mathrm{Simplify}\\5x\le \:30[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}5\\\frac{5x}{5}\le \frac{30}{5}[/tex]
[tex]x\le \:6[/tex]
The graph of the inequality [tex]x\le \:6[/tex] is shown below.
According with the graph the solutions are less than or equal to 6, using interval notation [tex](-\infty \:,\:6][/tex].
The solutions of [tex]5x-10\le \:20[/tex] are [tex](-\infty \:,\:6][/tex], so C is the correct answer.
