Question

Define a variable, write an inequality, and solve the problem. Check your solution. The difference of a number and 4 is no more than 8.

Short answer

The inequality is $x-4\le 8$and the solution of inequality is$x\le 12$.

Step-by-step solution

Step 1. Define a variable and write an inequality to describe the given information.

Let the number be $x$. The difference of a number and 4 is $x-4$. The phrase no more than means the same as less than or equal to. Therefore, the inequality is $x-4\le 8$

Step 2. Write subtraction property of inequalities.

For all numbers $p,q$and $r$, following are true.

(i) If $p>q$, then $p-r>q-r$.

(ii) If $p<q$, then $p-r<q-r$.

Step 3. Solve the obtained inequality, x−4≤8.

Use subtraction property of inequalities to solve the given inequalities.

$\begin{array}{c}x-4\le 8\\ x-4+4\le 8+4\\ x\le 12\end{array}$

Therefore, the solution $x-4\le 8$of is $x\le 12$.

Step 4. Check the solution.

To check the obtained solution, substitute a number less than as $x\le 12$in the inequality $x-4\le 8$, if the condition obtained is true, the solution is correct and if the condition obtained is false, the solution is incorrect.

Let $x=10$, as $x=10$. Substitute 10 for $x$into $x-4\le 8$.

$\begin{array}{c}x-4\le 8\\ 10-4\le 8\\ 6\le 8\end{array}$

As, the condition obtained$6\le 8$ is true, therefore the solution is correct.