Solve for $x$:
$$ \displaystyle \frac{60x - 20}{16} = 4x - 2$$
Then what must $x$ equal?
$\endgroup$ 12 Answers
$\begingroup$If I'm correctly interpreting you, you want to solve $$\frac{60x-20}{16}=4x-2.$$ Note that the numerator and denominator on the left have $4$ as a common factor, so dividing both numerator and denominator by $4$ gives us the equivalent $$\frac{15x-5}4=4x-2.$$ At this point, I recommend multiplying both sides by $4$ and solving.
$\endgroup$ $\begingroup$$$ \frac{60x - 20}{16} = 4x - 2 \\ $$
$$ \color{blue}{16} \cdot \frac{60x - 20}{16} = \color{blue}{16} \cdot (4x - 2) $$ $$ 60x - 20 = 16(4x - 2) $$ $$ 60x - 20 = 16 \cdot 4x - 16 \cdot 2 $$ $$ 60x - 20 = 64x - 32 $$ $$ 60x - 20 - \color{green}{60x} = 64x - 32 - \color{green}{60x} $$ $$ - 20 = 4x - 32 $$ $$ - 20 + \color{orange}{32} = 4x - 32 + \color{orange}{32} $$ $$ 12 = 4x $$ $$ \frac{12}{\color{blue}{4}} = \frac{4x}{\color{blue}{4}} $$ $$ 3 = x $$
Alternatively:
$$ \frac{60x - 20}{16} = 4x - 2 \\ $$ $$ \frac{4(15x - 5)}{16} = 4x - 2 $$ $$ \frac{15x - 5}{4} = 4x - 2 $$ $$ \color{blue}{4} \cdot \frac{15x - 5}{4} = \color{blue}{4}(4x - 2) $$ $$ 15x - 5 = 16x - 8 $$ $$ 15x - 5 - \color{green}{15x} = 16x - 8 - \color{green}{15x} $$ $$ -5 = x - 8 $$ $$ -5 + \color{orange}{8} = x - 8 + \color{orange}{8} $$ $$ 3 = x - 8 + 8 $$ $$ 3 = x $$
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