Question

write and solve two - step inequalities (homework)
solve each inequality. graph the solution set on a number line.

1. (2x+3>11)
2. (6x - 5geq23)
3. (12leq3x - 6)
4. (-3<4x + 1)
5. (-8x + 4leq-12)
6. (\frac{x}{3}-2>-1)
7. a rental company charges $15 plus $4 per hour to rent a bicycle. if margie does not want to spend more than $27 for her rental, write and solve an inequality to determine how many hours she can rent the bicycle and not spend more than $27. interpret the solution.

inequality: (4x + 15leq27)
solve:

Explanation:

Step1: Isolate the variable - term

For the inequality \(4x + 15\leq27\), subtract 15 from both sides. Using the subtraction - property of inequalities, \(4x+15 - 15\leq27 - 15\), which simplifies to \(4x\leq12\).

Step2: Solve for \(x\)

Divide both sides of the inequality \(4x\leq12\) by 4. By the division - property of inequalities, \(\frac{4x}{4}\leq\frac{12}{4}\), so \(x\leq3\).

Answer:

The solution of the inequality \(4x + 15\leq27\) is \(x\leq3\). On a number line, we draw a closed circle at 3 (because the inequality includes equality) and shade to the left of 3 to represent all the values of \(x\) that satisfy the inequality.