Question

Solve -5x - 3 >= 2 or 4x - 2 >= 5 and write the solution in interval notation. Use improper fractions if necessary.

Answer 1

Given the system of linear inequalities as;

$-5x-3\ge2,4x-2\ge5$

Solving the first inequality, we have;

$\begin{gathered} -5x-3\ge2 \\ -5x\ge2+3 \\ -5x\ge5 \\ x\leq\frac{5}{-5} \\ x\leq-1 \end{gathered}$

Also, solving the second inequality, we have;

$\begin{gathered} 4x-2\ge5 \\ 4x\ge5+2 \\ 4x\ge7 \\ x\ge\frac{7}{4} \end{gathered}$

Combine the intervals, we have;

$x\leq-1\text{ or x}\ge\frac{7}{4}$

The solution in interval notation is;

$(-\infty,-1\rbrack\cup\lbrack\frac{7}{4},\infty)$