Question

twelve less than 5 times a number is greater than or equal to 6 more than twice the number. Which inequality and number line represents the solutions for the given solution

Answer 1

The answer to the question

Answer 2

x ≥ 6

Explanation:

Here we have to convert the verbal expression to algebraic expression.

Word Algebraic

Less than -

Times *

Greater than or equal ≥

Twice 2

The given verbal expression is "twelve less than 5 times a number is greater than or equal to 6 more than twice the number. "

Let "x" be a number.

5x - 12 ≥ 6 + 2x

Now we have to isolate the variable and constants.

Add 12 from both sides, we get

5x - 12 + 12 ≥ 6 + 2x + 12

5x ≥ 2x +18

Now subtract 2x from both sides, we get

5x - 2x ≥ 2x - 2x + 18

3x ≥ 18

Divide both sides by 3, we get

`(3x)/(3) \geq (18)/(3)`

x ≥ 6

Now let's graph the inequality.

To draw the inequality, mark 6 on the number line with filled circle because the solution includes 6 and draw the arrow line to the right because it is greater than.