Question

Consider the following compound inequality. 4x+4_<-20 or 2x-3>5.A) Solve the inequality for x. B) Graph the compound inequality. C) Enter the solution in interval notation.

Answer 1

Given the inequalities

`\begin{gathered} 4x+4\leq-20\text{ ---- 1} \\ 2x-3>5\text{ ------ 2} \end{gathered}`

From (1),

`\begin{gathered} 4x+4\leq-20 \\ \text{collect like terms} \\ 4x\leq-20-4 \\ 4x\leq-24 \\ \text{divide both sides by the coefficient of x, which is 4} \\ (4x)/(4)\leq-(24)/(4) \\ x\leq-6 \end{gathered}`

From (2)

`\begin{gathered} 2x-3>5 \\ \text{collect like terms} \\ 2x>5+3 \\ 2x>8 \\ divide\text{ both sides by the co}efficient\text{ of x, which is 2} \\ (2x)/(2)>(8)/(2) \\ x>4 \end{gathered}`

A) Thus, for the above inequalities, the solution is expressed as

`x>4,\text{ x}\leq-6`

B) Graph of the compound inequality is as shown below

C) Solution in interval form

`(-\infty,-6\rbrack\text{ }\cup\text{ (4,}\infty)`