solve:%0A5x%20-%203%C2%A0%E2%89%A4%2012%0A*%0A2%20points%0Ax%20%E2%89%A4%201.8%0Ax%20%E2%89%A4%203%0Ax%20%E2%89%A4%2075%0Ax%20%E2%89%A4%2045

Answer 1

To solve this system of inequalities, we need to find the values of x that satisfy all four inequalities.

First, let's solve the first inequality: 5x - 3 ≤ 12.

To isolate x, we first add 3 to both sides:
5x - 3 + 3 ≤ 12 + 3
5x ≤ 15

Then, we divide both sides by 5 to solve for x:
(5x)/5 ≤ 15/5
x ≤ 3

Now, let's solve the second set of inequalities:

For x ≤ 1.8, x can be any value less than or equal to 1.8.

For x ≤ 3, x can be any value less than or equal to 3.

For x ≤ 75, x can be any value less than or equal to 75.

For x ≤ 45, x can be any value less than or equal to 45.

To find the values of x that satisfy all four inequalities, we need to find the intersection of the solution sets. The largest value that satisfies all four inequalities is the highest common value of x.

From the set of restrictions, we see that the maximum value of x is 3, as it satisfies the x ≤ 3 inequality.
Therefore, the solution to the system of inequalities is x ≤ 3.