Question
Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line. \( 2 x+4<10 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 of 1 A. The solution set is \( \square \). (Type your answer using interval notation.) B. The solution set is \( \varnothing \). W an example Get more help -
Ask by Howell Ramos. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is \((- \infty, 3)\).
Solution
Solve the equation \( 2x+4<10 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(2x+4<10\)
- step1: Move the constant to the right side:
\(2x<10-4\)
- step2: Subtract the numbers:
\(2x<6\)
- step3: Divide both sides:
\(\frac{2x}{2}<\frac{6}{2}\)
- step4: Divide the numbers:
\(x<3\)
The solution to the inequality \(2x+4<10\) is \(x<3\).
Now, let's express the solution set in interval notation. The solution set is all real numbers less than 3, which can be expressed as \((-\infty, 3)\).
Therefore, the correct choice is:
A. The solution set is \((- \infty, 3)\).
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Simplify this solution Mind Expander
To solve the inequality \( 2x + 4 < 10 \), we first subtract 4 from both sides: \( 2x < 6 \). Then, we divide both sides by 2, giving us \( x < 3 \). In interval notation, the solution set is expressed as \( (-\infty, 3) \). For the number line representation, you would draw a line and place an open circle at 3, shading all the area to the left to signify all values less than 3 are included in the solution set. This visually indicates that the solutions extend indefinitely towards negative infinity!
