A quarter of five less than a number is no more than a third of five more than the same number.
Which of the following inequalities fits the description above?
(1 point)
x−14×5≤x+13×5
14(x−5)≤13(x+5)
14(5−x)≤13(5+x)
14×5−x≤13×5+x
thank you sooooo much
To solve this problem, let's break it down step-by-step:
Step 1: Assume the number is x.
Step 2: "A quarter of five less than a number" can be written as (1/4)(x - 5).
Step 3: "Is no more than a third of five more than the same number" can be written as (1/3)(x + 5).
Step 4: Combine the previous two expressions to create the inequality:
(1/4)(x - 5) ≤ (1/3)(x + 5).
Step 5: Multiply both sides of the inequality by 12 to eliminate the fractions:
3(x - 5) ≤ 4(x + 5).
Step 6: Distribute and simplify:
3x - 15 ≤ 4x + 20.
Step 7: Subtract 3x from both sides:
-15 ≤ x + 20.
Step 8: Subtract 20 from both sides:
-35 ≤ x.
So, the correct inequality that fits the description above is:
x ≥ -35.
Therefore, the correct option is none of the provided inequalities.
To solve this question, we need to break down the given information and translate it into an inequality.
Let's start with the phrase "a quarter of five less than a number." This means we need to take a number and subtract 5 from it, and then find a quarter of that result.
Let's say the number is represented by x. So, a quarter of five less than the number can be written as (1/4)(x - 5).
Now, let's move on to the phrase "is no more than a third of five more than the same number." This means we need to take the number and add 5 to it, then find a third of that result.
Using the same variable x to represent the number, a third of five more than the number can be written as (1/3)(x + 5).
Putting it all together, we can write the inequality as:
(1/4)(x - 5) ≤ (1/3)(x + 5)
Now, let's check which of the given options matches this inequality:
1) x - 14 × 5 ≤ x + 13 × 5
2) 14(x - 5) ≤ 13(x + 5)
3) 14(5 - x) ≤ 13(5 + x)
4) 14 × 5 - x ≤ 13 × 5 + x
None of the given options match the inequality we derived. Therefore, none of the options fit the description above.
First, learn how to type fractions!
five less than a number ... x-5
a quarter of that ... 1/4 (x-5)
Now finish it off