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What is the solution to [tex]-\frac{3}{5}x + 4 \ \textgreater \ 1[/tex]?
A. [tex]x \ \textgreater \ -5[/tex] B. [tex]x \ \textless \ -5[/tex] C. [tex]x \ \textgreater \ 5[/tex] D. [tex]x \ \textless \ 5[/tex]
Let's solve the inequality [tex]\(-\frac{3}{5}x + 4 > 1\)[/tex] step-by-step.
1. Isolate the x-term:
First, subtract 4 from both sides of the inequality to start isolating the term containing [tex]\(x\)[/tex]: [tex]\[
-\frac{3}{5}x + 4 - 4 > 1 - 4
\][/tex] Simplifying this expression, we get: [tex]\[
-\frac{3}{5}x > -3
\][/tex]
2. Eliminate the coefficient of x:
To eliminate the coefficient, we can multiply both sides of the inequality by the reciprocal of [tex]\(-\frac{3}{5}\)[/tex], which is [tex]\(-\frac{5}{3}\)[/tex]. However, when multiplying by a negative number, we must reverse the inequality sign: [tex]\[
x < -3 \times -\frac{5}{3}
\][/tex]
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