Question

Solve the inequality for x in terms of a. Ax - 8 less than or equal to 12

Answer 1

`\large\boxed{\left\{\begin{array}{ccc}x\leq(20)/(a)&\text{for}\ a>0\\\\x\geq(20)/(a)&\text{for}\ a<0\end{array}\right }`

Explanation:

`ax-8\leq12\qquad\text{add 8 to both sides}\\\\ax-8+8\leq12+8\\\\ax\leq20\qquad\text{divide both sides by}\ a\\eq0\\\\(1)\ \text{if}\ a>0,\ \text{then:}\\\\x\leq(20)/(a)\\\\(2)\ \text{if}\ a<0,\ \text{then you must flip the sign of inequality:}\\\\x\geq(20)/(a)`