Express the set $$ -4 x+30 \leq 2 x+12 $$ using interval notation.

Question

UpStudy AI · Accepted Answer

To solve the inequality $$ -4x + 30 \leq 2x + 12 $$ and express the solution in interval notation, follow these steps:

1. **Combine like terms:**
   $$
   -4x + 30 \leq 2x + 12
   $$
   Subtract $$ 2x $$ from both sides:
   $$
   -6x + 30 \leq 12
   $$
   Subtract $$ 30 $$ from both sides:
   $$
   -6x \leq -18
   $$

2. **Solve for $$ x $$:**
   Divide both sides by $$ -6 $$. Remember to reverse the inequality sign when dividing by a negative number:
   $$
   x \geq 3
   $$

3. **Express in interval notation:**
   $$
   [3, \infty)
   $$

**Final Answer:**
$$\boxed{\,\left[\,3,\;\infty\,\right)}$$
The solution is $$ x \geq 3 $$, which in interval notation is $$[3, \infty)$$.

Express the set using interval notation.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Algebra Questions