To find which inequality represents all the solutions of [tex]\(10(3x + 2) > 7(2x - 4)\)[/tex], let's solve it step-by-step:
1. Expand both sides:
[tex]\[
10(3x + 2) > 7(2x - 4)
\][/tex]
Applying the distributive property:
[tex]\[
30x + 20 > 14x - 28
\][/tex]
2. Isolate terms involving [tex]\(x\)[/tex] on one side:
Subtract [tex]\(14x\)[/tex] from both sides:
[tex]\[
30x - 14x + 20 > 14x - 14x - 28
\][/tex]
Simplify:
[tex]\[
16x + 20 > -28
\][/tex]
3. Isolate the constant term:
Subtract 20 from both sides:
[tex]\[
16x + 20 - 20 > -28 - 20
\][/tex]
Simplify:
[tex]\[
16x > -48
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 16:
[tex]\[
\frac{16x}{16} > \frac{-48}{16}
\][/tex]
Simplify:
[tex]\[
x > -3
\][/tex]
The correct answer which represents all the solutions of the inequality [tex]\(10(3x + 2) > 7(2x - 4)\)[/tex] is:
C. [tex]\(x > -3\)[/tex]
