How do you write an inequality and solve given "the sum of nine times a number and fifteen is less than or equal to the sum of twenty four and ten times the number"?

Question

Eva Abramson · Accepted Answer

The inequality for this is #9x+15<=24+10x#.

Now that we know what our inequality is, we can now solve for #x#. To do this, we have to subtract 24 from each side: #9x+15-24<=24+10x-24# #9x-9<=10x# Next, let's subtract #9x# from each side: #9x-9-9x<=10x-9x# #-9<=9x# Finally, let's divide each side by 9 to get our answer: #-9/9<=(9x)/9# #-1<=x#

Hazel Anglin · Answer

undefined To write the inequality and solve it, we can first translate the given statement into mathematical language. Let's denote the unknown number as $x$.

The sum of nine times the number and fifteen is represented as $9x + 15$.

The sum of twenty-four and ten times the number is represented as $24 + 10x$.

The given statement states that $9x + 15$ is less than or equal to $24 + 10x$.

So, the inequality is $9x + 15 \leq 24 + 10x$.

To solve for $x$, we'll first isolate $x$ on one side of the inequality:

$$9x + 15 \leq 24 + 10x$$

Subtract $9x$ from both sides:

$$15 \leq 24 + x$$

Subtract $24$ from both sides:

$$15 - 24 \leq x$$

Simplify:

$$-9 \leq x$$

So, the solution to the inequality is $x \geq -9$.