Sure, let's solve the inequalities step-by-step.
First, we need to solve the inequality [tex]\(4x + 2 \leq 14\)[/tex].
1. Start with the inequality:
[tex]\[4x + 2 \leq 14\][/tex]
2. Subtract 2 from both sides of the inequality:
[tex]\[4x \leq 12\][/tex]
3. Divide both sides by 4:
[tex]\[x \leq 3\][/tex]
Next, we solve the inequality [tex]\(-21x + 1 < 22\)[/tex].
1. Start with the inequality:
[tex]\[-21x + 1 < 22\][/tex]
2. Subtract 1 from both sides of the inequality:
[tex]\[-21x < 21\][/tex]
3. Divide both sides by [tex]\(-21\)[/tex] (remember, when dividing by a negative number, the inequality sign reverses):
[tex]\[x > -1\][/tex]
Now, we combine the results of both inequalities.
From the first inequality, we have:
[tex]\[x \leq 3\][/tex]
From the second inequality, we have:
[tex]\[x > -1\][/tex]
Combining these results, we get:
[tex]\[-1 < x \leq 3\][/tex]
Hence, the solution to the inequality is:
[tex]\[-1 < x \leq 3\][/tex]
