Answer: C) [tex]x\geq1\frac{1}{2}[/tex]
Step-by-step explanation:
Let's solve your inequality step-by-step.
[tex]4x-7\geq \frac{-12x+14}{4}[/tex]
Step 1: Simplify both sides of the inequality.
[tex]4x-7\geq -3x +\frac{7}{2}[/tex]
Step 2: Add 3x to both sides.
[tex]4x+3x-7\geq -3x+3x +\frac{7}{2}\\7x-7\geq\frac{7}{2}[/tex]
Step 3: Add 7 to both sides.
[tex]7x-7+7\geq\frac{7}{2} +7\\7x\geq\frac{21}{2}[/tex]
Step 4: Multiply both sides by [tex]\frac{1}{7}[/tex].
[tex]7x(\frac{1}{7}) \geq\frac{21}{2} (\frac{1}{7}) \\x\geq\frac{21}{14} \\x\geq 1\frac{1}{2}[/tex]
