To solve the inequality, we can begin by simplifying the expression on the left side:
3/7x + 1/7 ≤ 6/7
To combine the fractions on the left side, we need a common denominator. In this case, the common denominator is 7:
(3/7)x + 1/7 ≤ 6/7
Now that the fractions have a common denominator, we can add the numerators:
(3x + 1)/7 ≤ 6/7
To get rid of the fractions, we can multiply both sides of the inequality by 7:
7 * (3x + 1)/7 ≤ (6/7) * 7
This simplifies to:
3x + 1 ≤ 6
Next, we can subtract 1 from both sides to isolate the term with x:
3x + 1 - 1 ≤ 6 - 1
This simplifies to:
3x ≤ 5
Finally, we can divide both sides of the inequality by 3 to solve for x:
(3x)/3 ≤ 5/3
This simplifies to:
x ≤ 5/3
Therefore, the solution to the inequality is x ≤ 5/3.
3/7x + 1/7 1 ≤ 6/7
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