 Determine whether the given problem is an equation or an expression. If it is an pedzenekO 2021-09-18 Answered
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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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
$$\displaystyle{x}=−{\frac{{{25}}}{{{4}}}}$$