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Chapter 0: Problem 94

Use interval notation to represent all values of \(x\) satisfying the given conditions. \(y=2 x-11+3(x+2)\) and \(y\) is at most 0

Short Answer

Expert verified
The values of \(x\) that satisfy the given conditions are represented by the interval \([1, \infty)\).

Step by step solution

01

Combine Like Terms

Simplify the equation by combining like terms. To do this, distribute the 3 into the term \(3(x+2)\) and combine the result with the remaining terms to give an expression: \(y=2x-11+3x+6\).
02

Simplify Equation

Combine the \(x\) terms and constant terms to simplify the equation further: \(y=5x-5\).
03

Set up Inequality

According to the problem, \(y\) is at most 0, meaning \(y \leq 0\). Replace \(y\) with 0 in the simplified equation and change the equation to an inequality: \(0 \leq 5x - 5\).
04

Solve for x

First, add 5 to both sides of the inequality to get \(5 \leq 5x \). Then, divide both sides by 5 to isolate \(x\): \(x \geq 1\).
05

Write Answer in Interval Notation

The solution \(x \geq 1\) in interval notation is \([1, \infty)\). This means \(x\) can take any value from 1 to infinity, inclusive of 1.

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