9514 1404 393
Answer:
3 < x < 6
Step-by-step explanation:
Use the perimeter formula to write an expression for the perimeter. Then put that in an inequality with the given limits. Solve for x.
P = 2(L +W)
P = 2((4x) +(2x +1)) = 2(6x +1) = 12x +2 . . . . . fill in the given values; simplify
The perimeter wants to be between 38 and 74 cm, so we have ...
38 < 12x +2 < 74
36 < 12x < 72 . . . . . subtract 2
3 < x < 6 . . . . . . . . . divide by 6
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<em>Additional comment</em>
Solving a compound inequality is very much like solving a single inequality. You need to "undo" what is done to the variable. The rules of equality (ordering) still apply. If you were to multiply or divide by a negative number, the direction (sense) of the inequality symbols would reverse in the same way they do for a single inequality.
Here, our first step was to subtract 2 from all parts of the inequality:
38 -2 < 12x +2 -2 < 74 -2 ⇒ 36 < 12x < 72
The division by 12 worked the same way: all parts are divided by 12.
36/12 < (12x)/12 < 72/12 ⇒ 3 < x < 6
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If it makes you more comfortable, you can treat the perimeter limits as two separate inequalities: 38 < 12x+2 and 12x+2 < 74. Both restrictions apply, so the solution set is the intersection of the solution sets of these separate inequalities.
Answer is x² + 2x + 5
<u>Step-by-step explanation:</u>
Step 1:
Add the two polynomials
⇒ (2x + 7) + (x² - 2) = 2x + 7 + x² - 2 = x² + 2x + 5
4 1/3:7 can be written in many ways
13:21 is the simplest form in whole numbers
Hope this helps! ;)
To eliminate all of the fractions in an equation, we can multiply the equation by the least common denominator of all of the fractions in the equation. To find the LCD, we need to find a number that has at least all of the factors of each of the denominators.
To find the LCD of the fractions in this equation, let's look at our denominators, 3 and 6. We can say 3 = 3 and 6 = 2 * 3. By examining this, we can see that our LCD <em>has to have </em>a 3 and 2, since those numbers are found in at least one of the fractions. Thus, our LCD is 3 * 2 = 6.
Now we know to multiply our entire equation by 6. This is solved as shown:
Our answer is 4x + 42 = 5.
