Question

1. solve for x.

$6x - \frac{4}{7}(21x - 35) = 2$
show your work here
$\bigcirc \\ x = \frac{11}{3}$ $\bigcirc \\ x = 3$
$\bigcirc \\ x = -3$ $\bigcirc \\ x = -\frac{11}{3}$

Explanation:

Step1: Distribute the fraction

First, distribute $\frac{4}{7}$ to the terms inside the parentheses:
$$6x - \frac{4}{7}(21x) + \frac{4}{7}(35) = 2$$
Calculate each term: $\frac{4}{7} \times 21x = 12x$ and $\frac{4}{7} \times 35 = 20$. So the equation becomes:
$$6x - 12x + 20 = 2$$

Step2: Combine like terms

Combine the $x$ terms: $6x - 12x = -6x$. Now the equation is:
$$-6x + 20 = 2$$

Step3: Isolate the variable term

Subtract 20 from both sides:
$$-6x = 2 - 20$$
$$-6x = -18$$

Step4: Solve for x

Divide both sides by -6:
$$x = \frac{-18}{-6}$$
$$x = 3$$

Answer:

$x = 3$ (corresponding to the option "x = 3")