Question

Ik its 16 but which inequality sign

Answer 1

None of the answer choices

Explanation:

Answer 2

x ≥ 4

Explanation:

The given statement is "The difference of 10 and a number is at most six".

Let "x" be the unknown number.

"The difference of 10 and a number" can be represented as either "10 - x" or "x - 10", depending on whether x < 10 or x > 10.

"Is at most six" means it is less than or equal to six.

Therefore, we have two potential cases:

`\begin{minipage}{3 cm}\underline{\sf Case\;1}:\;\textsf{If $x < 10$}\\\\\boxed{10 - x \leq 6}\end{minipage} \qquad \qquad\begin{minipage}{3 cm}\underline{\sf Case\;2}:\;\textsf{If $x > 10$}\\\\\boxed{x-10 \leq 6}\end{minipage}`

Solving the inequalities:

`\boxed{\begin{aligned}\underline{\sf Case\;1}\\\\10 - x &\leq 6\\10 - x-10 &\leq 6-10\\-x &\leq -4\\x &\geq 4\end{aligned}}`
`\boxed{\begin{aligned}\underline{\sf Case\;2}\\\\x-10&\leq 6\\x-10+10 &\leq 6+10\\x &\leq 16\\\\\end{aligned}}`

[Remember that when dividing both sides of an inequality by a negative number, we have to reverse the inequality sign.]

Therefore, the two possible solutions are:

• x ≥ 4
• x ≤ 16

If we take the statement "the difference between 10 and a number" as "10 - x" then the solution is x ≥ 4.