Question

his scale
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topic: inequalities
e, then graph this inequality: (\frac{x}{3}+\frac{5}{6} geq \frac{x}{2}+\frac{1}{3})

longer problems

topic: bedmas fractions
tis expression. show your work.

1. topic: bedmas fractions

Explanation:

Step1: Eliminate fractions by LCM

The denominators are 3, 6, 2. LCM of 3, 6, 2 is 6. Multiply each term by 6:
$$6\times\frac{x}{3}+6\times\frac{5}{6}\geq6\times\frac{x}{2}+6\times\frac{1}{3}$$
Simplify each term:
$$2x + 5\geq3x + 2$$

Step2: Isolate variable terms

Subtract \(2x\) from both sides:
$$2x - 2x + 5\geq3x - 2x + 2$$
Simplify:
$$5\geq x + 2$$

Step3: Solve for \(x\)

Subtract 2 from both sides:
$$5 - 2\geq x + 2 - 2$$
Simplify:
$$3\geq x$$
Or \(x\leq3\)

Answer:

The solution to the inequality \(\frac{x}{3}+\frac{5}{6}\geq\frac{x}{2}+\frac{1}{3}\) is \(x\leq3\). To graph it, draw a number line, plot a closed circle at 3 (since the inequality is "less than or equal to"), and shade to the left of 3.