Solve each open sentence.
x-5/9<or=to2x/15-2/5
To solve the inequality x - 5/9 ≤ 2x/15 - 2/5, we need to isolate the variable x on one side of the inequality sign. Here's how you can do it step by step:
Step 1: Multiply through by the least common denominator (LCD), which is 45, to eliminate the fractions. This is done to avoid dealing with fractions in the inequality.
45(x - 5/9) ≤ 45(2x/15 - 2/5)
Step 2: Simplify both sides of the inequality.
45x - 25 ≤ 6x - 18
Step 3: Get all the x terms on one side and the constant terms on the other side.
45x - 6x ≤ -18 + 25
39x ≤ 7
Step 4: Divide both sides of the inequality by the coefficient of x, which is 39.
x ≤ 7/39
Step 5: Simplify the fraction, if needed.
x ≤ 1/3 (rounded to the nearest thousandths)
Therefore, the solution to the inequality x - 5/9 ≤ 2x/15 - 2/5 is x ≤ 1/3.