Certainly! Let's solve the inequality step by step and identify the missing step:
We start with the given inequality:
[tex]\[
-x - 3 < 13 + 3x
\][/tex]
Step 1: Move all terms involving [tex]\( x \)[/tex] to one side and the constants to the other side. To do this, subtract [tex]\( 3x \)[/tex] from both sides:
[tex]\[
-x - 3 - 3x < 13 + 3x - 3x
\][/tex]
This simplifies to:
[tex]\[
-x - 3x - 3 < 13
\][/tex]
Step 2: Combine like terms on the left side:
[tex]\[
-4x - 3 < 13
\][/tex]
This is the missing step, which is identified as:
[tex]\[
-4x - 3 < 13
\][/tex]
Step 3: Isolate the [tex]\( x \)[/tex]-term by moving the constant term to the other side. To do this, add 3 to both sides of the inequality:
[tex]\[
-4x - 3 + 3 < 13 + 3
\][/tex]
Simplifying this, we get:
[tex]\[
-4x < 16
\][/tex]
Step 4: Solve for [tex]\( x \)[/tex] by dividing both sides of the inequality by -4. Remember to reverse the inequality sign when dividing by a negative number:
[tex]\[
\frac{-4x}{-4} > \frac{16}{-4}
\][/tex]
This simplifies to:
[tex]\[
x > -4
\][/tex]
So, the missing step in the solution to the inequality [tex]\(-x - 3 < 13 + 3x\)[/tex] is:
[tex]\[
-4x - 3 < 13
\][/tex]
And the final solution is:
[tex]\[
x > -4
\][/tex]
