Solve
4
7
x−
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.
To solve this inequality, we need to isolate the variable x.
Given: (4/7)x - (2/7) > 5/7
Add (2/7) to both sides of the inequality:
(4/7)x > (5/7) + (2/7)
(4/7)x > (7/7)
Simplify the right side:
(4/7)x > 1
To isolate x, divide both sides by (4/7), being careful to flip the inequality sign since we are dividing by a negative number:
x < (1)/(4/7)
Simplify the right side by multiplying by the reciprocal:
x < 1 * (7/4)
x < 7/4
So, the solution to the inequality is x < 7/4, which can also be written as x < 1 3/4.
To solve the inequality:
4/7x - 2/7 > 5/7
First, let's get rid of the fraction by multiplying both sides of the inequality by the reciprocal of the coefficient of x, which is 7/4:
(7/4)(4/7x - 2/7) > (7/4)(5/7)
Simplifying:
(7/4)(4/7)x - (7/4)(2/7) > (7/4)(5/7)
Canceling out some terms:
x - 1/2 > 5/4
Now, let's isolate the variable x by adding 1/2 to both sides of the inequality:
x - 1/2 + 1/2 > 5/4 + 1/2
Simplifying:
x > 5/4 + 2/4
Combining the fractions:
x > 7/4
Therefore, the solution to the inequality is x > 7/4, which can be written as a mixed number as x > 1 and 3/4.
To solve the inequality, we want to isolate the variable x. Here are the steps to solve the given inequality:
1. Start by subtracting 2/7 from both sides of the inequality:
4/7 x - 2/7 > 5/7 - 2/7
Simplifying both sides, we get:
4/7 x - 2/7 > 3/7
2. Next, we want to get rid of the fraction by multiplying both sides of the equation by the reciprocal of the coefficient of x, which is 7/4:
(7/4)*(4/7)x - (7/4)*(2/7) > (7/4)*(3/7)
This simplifies to:
x - 2/4 > 21/28
3. Simplify both sides of the equation:
x - 1/2 > 3/4
4. To isolate x, add 1/2 to both sides of the inequality:
x - 1/2 + 1/2 > 3/4 + 1/2
This simplifies to:
x > 3/4 + 2/4
Simplifying further, we have:
x > 5/4
5. Expressing the rational number as a mixed number, we have:
x > 1 + 1/4
Therefore, the solution to the inequality is x > 1 1/4 or x > 5/4 as a mixed number.