Let's solve the inequality [tex]\( 54 - 10x \leq 20 + 7x \)[/tex] step-by-step.
1. Move all the [tex]\( x \)[/tex]-terms to one side of the inequality:
[tex]\[
54 - 10x \leq 20 + 7x
\][/tex]
Subtract [tex]\( 7x \)[/tex] from both sides:
[tex]\[
54 - 10x - 7x \leq 20
\][/tex]
Simplify:
[tex]\[
54 - 17x \leq 20
\][/tex]
2. Move all constant terms to the opposite side:
Subtract 54 from both sides:
[tex]\[
-17x \leq 20 - 54
\][/tex]
Simplify:
[tex]\[
-17x \leq -34
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides by -17 (note that dividing by a negative number reverses the inequality):
[tex]\[
x \geq 2
\][/tex]
4. Interpret the result:
The solution to the inequality is:
[tex]\[
x \leq 2
\][/tex]
Hence, the correct answer is:
C. [tex]\( x \leq 2 \)[/tex]
