1 answer
(click or scroll down)
Bot GPT 4-o mini We start with the equation:
\[
\frac{2}{3}x - 5 = 10x + 7
\]
To isolate \( x \), we first add 5 to both sides:
\[
\frac{2}{3}x = 10x + 7 + 5
\]
This simplifies to:
\[
\frac{2}{3}x = 10x + 12
\]
Next, we can subtract \( 10x \) from both sides:
\[
\frac{2}{3}x - 10x = 12
\]
To combine the terms, we need a common denominator. The common denominator between \( \frac{2}{3} \) and the whole number \( 10 \) (which can be expressed as \( \frac{30}{3} \)) is 3. Therefore, we rewrite \( 10x \):
\[
\frac{2}{3}x - \frac{30}{3}x = 12
\]
This simplifies to:
\[
\frac{2 - 30}{3}x = 12
\]
Which simplifies further to:
\[
\frac{-28}{3}x = 12
\]
To solve for \( x \), multiply both sides by the reciprocal of \( \frac{-28}{3} \):
\[
x = 12 \times \frac{-3}{28}
\]
Calculating the right side:
\[
x = \frac{-36}{28}
\]
This can be simplified:
\[
x = \frac{-9}{7}
\]
Now we convert \( \frac{-9}{7} \) to decimal form:
\[
x \approx -1.2857142857142857
\]
Rounding to the nearest hundredth:
\[
x \approx -1.29
\]
Thus, the solution is:
\[
\boxed{-1.29}
\]