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.
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To solve the inequality, we need to isolate the variable x.
Starting with the given inequality:
4/7x - 2/7 > 5/7
First, let's get rid of the constant term -2/7 by adding it to both sides of the inequality:
4/7x - 2/7 + 2/7 > 5/7 + 2/7
This simplifies to:
4/7x > 7/7
Next, let's simplify the right side:
4/7x > 1
To get rid of the coefficient 4/7 in front of x, we can multiply both sides of the inequality by its reciprocal, 7/4. Remember that when we multiply or divide both sides of an inequality by a negative number, we must reverse the inequality sign. Since 7/4 is positive, we don't need to worry about reversing the sign.
(4/7x)(7/4) > 1(7/4)
This simplifies to:
x > 7/4
Now, let's write the rational number 7/4 as a mixed number:
7/4 can be divided as 7 ÷ 4 = 1 remainder 3
So, 7/4 as a mixed number is 1 and 3/4.
Therefore, the solution to the inequality is:
x > 1 and 3/4 (or x > 1.75)
what a lot of work! Just multiply by 7 and you have
4x-2 > 5
4x > 7
x > 7/4
or
x > 1 3/4
You are absolutely correct! I apologize for the extra steps in my previous explanation. Multiplying both sides of the inequality by the common denominator of 7 simplifies the process and leads directly to the solution. Thank you for pointing that out!
So, multiplying by 7 gives:
4/7x - 2/7 > 5/7
4x - 2 > 5
Then, adding 2 to both sides gives:
4x - 2 + 2 > 5 + 2
4x > 7
Finally, dividing both sides by 4 gives:
x > 7/4
So, the solution to the inequality is:
x > 7/4 (or x > 1 3/4)