Question

1/4(x-2)=3 - (x+1/6)Select the equivalent expression.\left(\dfrac{3^{-6}}{7^{-3}}\right)^{5}=?(7−33−6 )5=?left parenthesis, start fraction, 3, start superscript, minus, 6, end superscript, divided by, 7, start superscript, minus, 3, end superscript, end fraction, right parenthesis, start superscript, 5, end superscript, equals, question markChoose 1 answer:Choose 1 answer:

Answer 1

Explanation: To solve the following equation

$\frac{1}{4}(x-2)=3-(x+\frac{1}{6})$

we will use a simple rule shown below

$\begin{gathered} \frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+c\cdot b}{b\cdot d} \\ or \\ \frac{a}{b}-\frac{c}{d}=\frac{a\cdot d-c\cdot b}{b\cdot d} \end{gathered}$

Above we can see how to sum or subtract fractions.

Step 1: Let's calculate as follows

$\begin{gathered} \frac{1}{4}(x-2)=3-(x+\frac{1}{6}) \\ \frac{x}{4}-\frac{2}{4}=3-x-\frac{1}{6} \\ \frac{x}{4}+x=3+\frac{2}{4}-\frac{1}{6} \\ \frac{x+4\cdot x}{4}=3+\frac{6\cdot2-4\cdot1}{4\cdot6} \\ \frac{x+4x}{4}=3+\frac{8}{24} \\ \frac{5x}{4}=\frac{3\cdot24+8}{24} \\ \frac{5x}{4}=\frac{72+8}{24} \\ \frac{5x}{4}=\frac{80}{24} \\ x=\frac{80\cdot4}{24\cdot5} \\ x=\frac{320}{120} \\ x=\frac{8}{3}\text{ or x }\cong2.667 \end{gathered}$

Final answer: So the final answer is x = 8/3 or x = 2.667