Question
Solve 5x+12.5<23.1 . Write the rational number in your answer in decimal form to the hundredths place. Make sure to wr
Answers
Answer
Solve 4/7x−2/7>5/7 . Write the rational number in your answer as a mixed number. Make sure to write your inequality so that x comes first.
Answered by
GPT 3.5
To isolate x in the inequality 5x + 12.5 < 23.1, we can start by subtracting 12.5 from both sides:
5x + 12.5 - 12.5 < 23.1 - 12.5
This simplifies to:
5x < 10.6
To solve for x, we divide both sides of the inequality by 5:
(5x)/5 < 10.6/5
This yields:
x < 2.12
Therefore, the solution to the inequality is x < 2.12.
5x + 12.5 - 12.5 < 23.1 - 12.5
This simplifies to:
5x < 10.6
To solve for x, we divide both sides of the inequality by 5:
(5x)/5 < 10.6/5
This yields:
x < 2.12
Therefore, the solution to the inequality is x < 2.12.
Answered by
GPT 3.5
To solve the inequality (4/7)x - 2/7 > 5/7, we will write the mixed number as an improper fraction and then solve for x.
Step 1: Convert mixed numbers to improper fractions.
In this case, the mixed number is already a fraction.
(4/7)x - 2/7 > 5/7
Step 2: Add the constant terms on both sides of the inequality.
On the left side, (4/7)x - 2/7 + 2/7 = (4/7)x
On the right side, 5/7 + 2/7 = 7/7 = 1
(4/7)x > 1
Step 3: Divide both sides of the inequality by 4/7.
Note: When you divide by a positive number, the inequality symbol remains the same. If you divide by a negative number, the inequality symbol changes direction.
(4/7)x / (4/7) > 1 / (4/7)
This simplifies to:
x > 1 / (4/7)
To divide by a fraction, we multiply the numerator by the reciprocal of the denominator:
x > 1 * (7/4)
x > 7/4
Therefore, the solution to the inequality is x > 7/4, which can be written as x > 1 3/4 as a mixed number.
Step 1: Convert mixed numbers to improper fractions.
In this case, the mixed number is already a fraction.
(4/7)x - 2/7 > 5/7
Step 2: Add the constant terms on both sides of the inequality.
On the left side, (4/7)x - 2/7 + 2/7 = (4/7)x
On the right side, 5/7 + 2/7 = 7/7 = 1
(4/7)x > 1
Step 3: Divide both sides of the inequality by 4/7.
Note: When you divide by a positive number, the inequality symbol remains the same. If you divide by a negative number, the inequality symbol changes direction.
(4/7)x / (4/7) > 1 / (4/7)
This simplifies to:
x > 1 / (4/7)
To divide by a fraction, we multiply the numerator by the reciprocal of the denominator:
x > 1 * (7/4)
x > 7/4
Therefore, the solution to the inequality is x > 7/4, which can be written as x > 1 3/4 as a mixed number.