Huang Powell
09/24/2023 · Junior High School
Solve the equation. \[ 2 x+7=2(x-12) \] The solution set is \( \square \). (Select "all real numbers" if applicable.) \( \begin{array}{cc}\{\square\} & \{\} \\ \begin{array}{c}\text { all real } \\ \text { numbers }\end{array} & \frac{\square}{\square}\end{array} \)
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Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( 2x+7=2(x-12) \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(2x+7=2\left(x-12\right)\)
- step1: Expand the expression:
\(2x+7=2x-24\)
- step2: Cancel equal terms:
\(7=-24\)
- step3: The statement is false:
\(x \in \varnothing \)
The solution set for the equation \(2x+7=2(x-12)\) is the empty set, denoted as \( \{\} \). This means that there are no real number solutions for this equation.
Quick Answer
The solution set is \( \{\} \).
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