Answer:
[tex] \displaystyle \large{x \leqslant 15}[/tex]
Step-by-step explanation:
We are given the Inequality:
[tex] \displaystyle \large{2x + 12 \leqslant 42}[/tex]
To solve an Inequality, solve it like an equation: We isolate x-term.
First, subtract 12 both sides.
[tex] \displaystyle \large{2x + 12 - 12 \leqslant 42 - 12} \\ \displaystyle \large{2x \leqslant 30}[/tex]
Then divide both sides by 2.
[tex] \displaystyle \large{ \frac{2x}{2} \leqslant \frac{30}{2} }[/tex]
Divide the like term. 2 divides 2 = 1; 2 divides 30 = 15.
[tex] \displaystyle \large{ \frac{ \cancel{2}x}{ \cancel{2}} \leqslant \frac{ \cancel{30}}{ \cancel{2}} } \\ \displaystyle \large{ \frac{ 1x}{ 1} \leqslant \frac{15}{1} }[/tex]
Generally, we do not recommend writing 1 as a denominator as we would just cancel 1 anyways.
That goes the same to 1x which we can simplify to x.
[tex] \displaystyle \large \boxed{ x \leqslant 15}[/tex]
Let me know if you have any questions!
