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.
Note: You will find the option to add a
>
>,
<
<,
≥
≥, or
≤
≤ symbol in the Comparison
(<)
(<) keyboard.
To solve the inequality, we want to isolate x. Starting with the given inequality:
4/7(x) - 2/7 > 5/7
First, we can add 2/7 to both sides:
4/7(x) > 5/7 + 2/7
4/7(x) > 7/7
Simplifying the right side:
4/7(x) > 1
Next, we can multiply both sides by the reciprocal of 4/7, which is 7/4:
(7/4)(4/7)(x) > (7/4)(1)
1(x) > 7/4
Simplifying the left side:
x > 7/4
Therefore, the solution to the inequality is x > 7/4.
To solve the inequality, 4/7 - 2/7 > 5/7, we can begin by combining the fractions on the left side of the inequality:
(4 - 2) / 7 > 5/7
Simplifying further, we have:
2/7 > 5/7
Since the denominators are equal, we can compare the numerators directly. Therefore, the inequality simplifies to:
2 > 5
However, 2 is not greater than 5, so this inequality is false. Thus, there is no solution for the inequality:
4/7 - 2/7 > 5/7
To solve the inequality, we will first isolate the variable x. Here's how we do it step by step:
1. Start with the given inequality: 4/7(x - 2/7) > 5/7.
2. Multiply both sides of the inequality by the reciprocal of the coefficient of x to remove the fraction. In this case, the reciprocal of 4/7 is 7/4. So, we have:
(7/4) * (4/7)(x - 2/7) > (7/4) * (5/7).
3. Simplify the expression:
(7/4)(4/7) * (x - 2/7) > (7/4)(5/7).
The fractions on both sides of the inequality cancel out, leaving us with:
1(x - 2/7) > (35/28).
4. Distribute the 1 on the left side of the equation:
x - 2/7 > 35/28.
5. Add 2/7 to both sides to solve for x:
x - 2/7 + 2/7 > 35/28 + 2/7.
x > 37/28.
The solution to the inequality is x > 37/28. This can also be written as a mixed number by dividing 37 by 28 and expressing any remaining fraction as a mixed number. The quotient is 1 and the remainder is 9/28. Therefore, the rational number is 1 9/28.