solve
-14 less than or equal to 4x+2 and 4x+2<22
Treat just like an equation, except if you multiply/divide by a negative, which means you must reverse the carat.
i don't understand how to do this problem...thats why im asking for help... i have not the slightest idea what to do
To solve the inequality equation "-14 less than or equal to 4x+2" and "4x+2<22," we need to isolate the variable x. Let's break it down step by step:
1. Solve the first inequality: -14 ≤ 4x + 2
- First, subtract 2 from both sides of the inequality:
-14 - 2 ≤ 4x + 2 - 2
-16 ≤ 4x
- Next, divide both sides by 4 (remember, when dividing or multiplying by a negative number, the inequality sign flips):
-16/4 ≤ 4x/4
-4 ≤ x
So, the first inequality can be rewritten as -4 ≤ x.
2. Solve the second inequality: 4x + 2 < 22
- First, subtract 2 from both sides of the inequality:
4x + 2 - 2 < 22 - 2
4x < 20
- Next, divide both sides by 4:
4x/4 < 20/4
x < 5
So, the second inequality can be rewritten as x < 5.
Combining both inequalities, we have -4 ≤ x < 5. This means that any value of x greater than or equal to -4 and less than 5 satisfies the given inequalities.