Question

solve for x -7x+1≥22 or -10x+41≥81

Answer 1

Answer:

The answer to the union of the two sets is: $x\leq -3$

Step-by-step explanation:

Since they are asking for an "OR" condition, we need to find the set of solutions for each inequality, and then use the union of those two sets.

First inequality:

$-7x+1\geq 22\\1-22\geq 7x\\-21\geq 7x\\-3\geq x\\x\leq -3$

so this is the set of all real numbers smaller than or equal to -3 (visualize the numbers on the number line to the left of -3 and including -3 itself)

Second inequality:

$-10x+41\geq 81\\41-81\geq 10x\\-40\geq 10x\\-4\geq x\\x\leq -4$

So, this sets consists of all real numbers smaller than or equal to -4 (visualize the numbers on the number line to the left of -4 and including -4 itself.

Then, when we do the union of these two sets, we get:

$x\leq -3$

since the number -4 is located to the left of -3 on the number line, so the set defined by the second inequality is in fact a subset of the one defined by the first inequality.