Question

solve the inequality, and graph the solution on a number line.
5x - 5 ≤ 6(x - 1)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution is
(type an inequality. simplify your answer.)
b. there is no solution.
c. the solution is all real numbers.
choose the correct graph of the solution.

Explanation:

Step1: Expand the right - hand side

$5x - 5\leqslant6x-6$

Step2: Move the terms with $x$ to one side

$5x-6x\leqslant - 6 + 5$

Step3: Simplify the inequality

$-x\leqslant - 1$

Step4: Multiply both sides by - 1 (reverse the inequality sign)

$x\geqslant1$

Answer:

A. The solution is $x\geqslant1$; The correct graph is a number - line with a closed circle at 1 and an arrow pointing to the right (not shown in the options provided in a complete way in the question but based on the solution $x\geqslant1$ it should be a closed - circle at 1 and right - pointing arrow).