Question

How do you solve and graph the inequalities 3(x + 3) - 2 < 4 or 1 - x ≤ -1?

Answer 1

To solve the given inequalities, distribute and combine like terms, then isolate x. Graph each inequality on a number line and shade the respective regions. Both solutions combined shade everything left of -1 and right of 2.

Step-by-step explanation:

To solve the inequality 3(x + 3) - 2 < 4, we first need to simplify and solve for x:

1. Distribute the 3 into the parentheses: 3x + 9 - 2 < 4.
2. Combine like terms: 3x + 7 < 4.
3. Subtract 7 from both sides: 3x < -3.
4. Divide by 3: x < -1.

To graph this inequality, draw a number line, plot a point at x = -1, and shade everything to the left of this point since x is less than -1.

For the second inequality 1 - x ≤ -1, follow these steps to solve:

1. Add x to both sides: 1 ≤ x - 1.
2. Add 1 to both sides: 2 ≤ x.

To graph this one, draw a number line, plot a point at x = 2, and shade everything to the right of this point since x is greater than or equal to 2.

Since the question asks for the solution of either inequality, we combine the graphs: everything to the left of -1 or to the right of 2 is shaded.