Question

Solve the inequality: -4x+4 < = -20. Write the solution using interval notation

Answer 1

Given the inequality:

$-4x+4\leqslant-20$

To solve the inequality for x, the first step is to subtract 4 from both sides of the inequality.

$\begin{gathered} -4x+4-4\leqslant-20-4 \\ -4x\leqslant-24 \end{gathered}$

Next, we divide both sides of the inequality by -4.

Note: When you divide or multiply by a negative number in inequality, the inequality sign reverses.

Therefore, we have:

$\begin{gathered} \frac{-4x}{-4}\geqslant\frac{-24}{-4} \\ x\geqslant6 \end{gathered}$

Next, we write our result in interval notation.

Since the value is greater than or equal to, we use the close bracket '['.

Therefore, the solution to the inequality in interval notation is:

$\lbrack6,\infty)$