-9/7x + 8 < -4x - 5
-9/7x + 4x + 8 , -4x + 4x - 5
-9/7x + 4x +8 < -5
The book then has
19/7x + 8 < - 5
I know how to solve this but I am lacking or trying to remeber how they got 19/7 - need a refresher
Convert the "x" terms to common denominators
4 x - (9/7) x = 28 x - (9/7) x
= (19/7) x
To convert the "x" terms to common denominators in the expression -9/7x + 4x + 8, we need to find a common denominator for -9/7 and 4. The least common denominator (LCD) of 7 and 1 is 7.
To convert -9/7 to a fraction with the denominator 7, we multiply both the numerator and denominator by 7:
(-9/7) * (7/1) = -63/7
So, the expression becomes:
-63/7x + 4x + 8
Now, we can simplify the expression:
-63/7x + 4x + 8 = (-63x + 4x) / 7 + 8 = (-59x) / 7 + 8
The "x" term has been converted to a fraction with a common denominator of 7. Now, we have:
(-59x) / 7 + 8 < -5
Next, to combine the fractions, we need to have a common denominator of 7 for both terms. The LCD is already 7, so we can proceed:
((-59x) / 7) + (8/1) < -5
Now, we can add the fractions:
((-59x) + (8 * 7)) / 7 < -5
((-59x) + 56) / 7 < -5
So, the expression becomes ((-59x) + 56) / 7 < -5.
Please note that this is the step before the book's expression of (19/7)x + 8 < -5. It seems there may have been an error or confusion in the given question.