Dolly Robinson

2021-09-27

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. $\frac{3}{4}\left(t-2\right)-\frac{2}{5}\left(2t-3\right)=\frac{1}{5}$

Nathanael Webber

Step 1
The given equation is $\frac{3}{4}\left(t-2\right)-\frac{2}{5}\left(2t-3\right)=\frac{1}{5}$
An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.
Step 2
Consider the equation $\frac{3}{4}\left(t-2\right)-\frac{2}{5}\left(2t-3\right)=\frac{1}{5}$.
It is a equation.
$\left(20\right)\frac{3}{4}\left(t-2\right)-\left(20\right)\frac{2}{5}\left(2t-3\right)=\left(20\right)\frac{1}{5}$ [lcm 4,5 is 20]
$15\left(t-2\right)-8\left(2t-3\right)=4$
$15t-30-16t+24-4=0$
$-t-10=0$
$t=-10$

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