Certainly! Let's solve the inequality step by step:
Problem: Solve the inequality [tex]\(4(3 - x) < 5x + 6\)[/tex].
Step 1: Distribute the 4 on the left side.
[tex]\[ 4(3 - x) < 5x + 6 \][/tex]
[tex]\[ 12 - 4x < 5x + 6 \][/tex]
Step 2: Move all terms involving [tex]\(x\)[/tex] to one side. To do this, subtract [tex]\(5x\)[/tex] from both sides.
[tex]\[ 12 - 4x - 5x < 6 \][/tex]
[tex]\[ 12 - 9x < 6 \][/tex]
Step 3: Move the constant term (12) to the other side by subtracting 12 from both sides.
[tex]\[ 12 - 12 - 9x < 6 - 12 \][/tex]
[tex]\[ -9x < -6 \][/tex]
Step 4: Divide by the coefficient of [tex]\(x\)[/tex], which is -9, noting that dividing by a negative number reverses the inequality sign.
[tex]\[ x > \frac{-6}{-9} \][/tex]
[tex]\[ x > \frac{2}{3} \][/tex]
So, the solution to the inequality [tex]\(4(3 - x) < 5x + 6\)[/tex] is [tex]\(x > \frac{2}{3}\)[/tex].
Finally, converting [tex]\(\frac{2}{3}\)[/tex] to its decimal form, we get:
[tex]\[ \frac{2}{3} \approx 0.6666666666666666 \][/tex]
Thus, [tex]\(x > 0.6666666666666666\)[/tex].
