Let's solve the inequality step-by-step.
We start with the given inequality:
[tex]\[
-4x + 7 > 19
\][/tex]
Step 1: Subtract 7 from both sides of the inequality to isolate the term with [tex]\( x \)[/tex].
[tex]\[
-4x + 7 - 7 > 19 - 7
\][/tex]
This simplifies to:
[tex]\[
-4x > 12
\][/tex]
Step 2: Divide both sides of the inequality by [tex]\(-4\)[/tex]. Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the direction of the inequality.
[tex]\[
x < \frac{12}{-4}
\][/tex]
[tex]\[
x < -3
\][/tex]
So, the original inequality [tex]\( -4x + 7 > 19 \)[/tex] is equivalent to:
[tex]\[
x < -3
\][/tex]
