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]
3. Simplify the multiplication:
Calculate [tex]\(-3 \times -\frac{5}{3}\)[/tex]:
[tex]\[
-3 \times -\frac{5}{3} = 5
\][/tex]
Therefore, our inequality becomes:
[tex]\[
x < 5
\][/tex]
So the solution to the inequality [tex]\(-\frac{3}{5}x + 4 > 1\)[/tex] is:
[tex]\[
x < 5
\][/tex]
Examining the provided choices:
A) [tex]\(x > -5\)[/tex]
B) [tex]\(x < -5\)[/tex]
C) [tex]\(x > 5\)[/tex]
D) [tex]\(x < 5\)[/tex]
The correct answer is:
D) [tex]\(x < 5\)[/tex]
