# Determine whether the given problem is an equation or an expression. If it is an

Determine whether the given problem is an equation or an expression. If it is an equation, then solve. If it is an expression, then simplify. 1/2 (2x - 1) - 1/3 (5x + 2) = 3

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Tuthornt
Step 1
Concept − A relation is an equation if it involves an equal sign.
And if it just involves polynomial function with no equal sign then it's an expression.
Given relation −
$$\displaystyle{\frac{{{1}}}{{{2}}}}{\left({2}{x}-{1}\right)}-{\frac{{{1}}}{{{3}}}}{\left({5}{x}+{2}\right)}={3}$$
Here, we see an equal sign representing the relation. Hence, this is an equation.
Step 2
Let's simplify this equation −
$$\displaystyle{\frac{{{1}}}{{{2}}}}{\left({2}{x}-{1}\right)}-{\frac{{{1}}}{{{3}}}}{\left({5}{x}+{2}\right)}={3}$$
$$\displaystyle{\frac{{{3}{\left({2}{x}-{1}\right)}-{2}{\left({5}{x}+{2}\right)}}}{{{6}}}}={3}$$
$$\displaystyle{3}{\left({2}{x}-{1}\right)}-{2}{\left({5}{x}+{2}\right)}={6}\times{3}$$
6x−3−10x−4 = 18
−4x−7 = 18
−4x = 18+7
−4x = 25
$$\displaystyle{x}=−{\frac{{{25}}}{{{4}}}}$$