To solve the inequality:
[tex]\[ x + 8 - 3x \geq 4x - (1 - 3x) \][/tex]
follow these steps:
1. Distribute the negative sign on the right side:
[tex]\[ x + 8 - 3x \geq 4x - 1 + 3x \][/tex]
2. Combine like terms:
[tex]\[ (x - 3x) + 8 \geq (4x + 3x) - 1 \][/tex]
[tex]\[ -2x + 8 \geq 7x - 1 \][/tex]
3. Move all terms involving [tex]\(x\)[/tex] to one side and constant terms to the other side:
[tex]\[ -2x - 7x \geq -1 - 8 \][/tex]
[tex]\[ -9x \geq -9 \][/tex]
4. Divide both sides by [tex]\(-9\)[/tex], remembering to reverse the inequality sign because we are dividing by a negative number:
[tex]\[ x \leq 1 \][/tex]
Therefore, the simplified inequality is:
[tex]\[ x \leq 1 \][/tex]
