solve inequality. write the solution set in interval notation
7x+6 greater than or equal to -(x-6)
add x to both sides, then subtract six from both sides.
To solve the inequality 7x + 6 ≥ -(x - 6), follow these steps:
Step 1: Distribute the negative sign inside the parentheses on the right side of the inequality:
7x + 6 ≥ -x + 6
Step 2: Combine like terms by adding x to both sides of the inequality:
7x + x + 6 ≥ 6
This simplifies to:
8x + 6 ≥ 6
Step 3: Subtract 6 from both sides of the inequality:
8x ≥ 0
Step 4: Divide both sides of the inequality by 8, remembering to flip the inequality symbol when dividing by a negative number:
x ≥ 0/8
Simplifying further:
x ≥ 0
Therefore, the solution set in interval notation is [0, ∞) which means that x is greater than or equal to 0.