Question

find all numbers such that a third of a number increased by half that number is at least 3 less than that same number

Answer 1

Answer:

All real numbers less than or equal to 18

Step-by-step explanation:

Let

x -----> the number

we know that

The algebraic expression that represent this situation is

$\frac{1}{3}x+\frac{1}{2}x \geq x-3$

Solve for x

Multiply by 6 both sides to remove the fractions

$2x+3x \geq6x-18$

Combine like terms left side

$5x \geq6x-18$

Adds 18 both sides

$5x+18 \geq 6x$

Subtract 5x both sides

$18 \geq 6x-5x$

$18 \geq x$

Rewrite

$x\leq 18$

All real numbers less than or equal to 18