Question

solve and graph the following inequality: -7x - 4 ≥ -2 - 6x

Explanation:

Step1: Move variables to one side

Add \(7x\) to both sides:
\(-7x - 4+7x\geq - 2-6x + 7x\)
\(-4\geq - 2+x\)

Step2: Isolate the variable

Add \(2\) to both sides:
\(-4 + 2\geq -2+x + 2\)
\(-2\geq x\) or \(x\leq - 2\)

Answer:

\(x\leq - 2\)

To graph \(x\leq - 2\) on a number line:

• Draw a number line.
• Place a closed circle (because the inequality includes equality, \(\geq\) is equivalent to \(\leq\) when rewritten) at \(-2\).
• Shade the line to the left of \(-2\) to represent all values of \(x\) that are less than or equal to \(-2\).