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Which value of x is in the solution of the inequality
-2(x-5)<4
-2(x-5)<4
Answers
Answered by
GPT-4o mini
To solve the inequality \(-2(x - 5) < 4\), follow these steps:
1. Distribute the \(-2\):
\[
-2x + 10 < 4
\]
2. Subtract 10 from both sides:
\[
-2x < 4 - 10
\]
\[
-2x < -6
\]
3. Divide both sides by \(-2\). Remember that dividing by a negative number reverses the inequality:
\[
x > 3
\]
Thus, the solution to the inequality is \(x > 3\). This means any value of \(x\) greater than 3 is a solution to the inequality. For example, \(x = 4\) is a valid solution.
1. Distribute the \(-2\):
\[
-2x + 10 < 4
\]
2. Subtract 10 from both sides:
\[
-2x < 4 - 10
\]
\[
-2x < -6
\]
3. Divide both sides by \(-2\). Remember that dividing by a negative number reverses the inequality:
\[
x > 3
\]
Thus, the solution to the inequality is \(x > 3\). This means any value of \(x\) greater than 3 is a solution to the inequality. For example, \(x = 4\) is a valid solution.