Question

1/3x +6 = 2x; 1/2(4x-2)=-7

Answer 1

$\frac{1}{3}x+6=2x$

$2x-\frac{1}{3}x=6$

$\frac{5}{3}x=6$

$x=6:\frac{5}{3}$

$x=6*\frac{3}{5}$

$x=\frac{18}{5}$

$\frac{1}{2}(4x-2)=-7$

$2x-1=-7$

$2x=-6$

$x=-6:2$

$x=-3$

Answer 2

To solve the given equations, we'll find the values of "x" that satisfy each equation one by one.

1. Equation 1: (1/3)x + 6 = 2x

Step 1: Eliminate the fraction by multiplying the entire equation by the common denominator, which is 3. 3 * ((1/3)x + 6) = 3 * 2x x + 18 = 6x

Step 2: Move all "x" terms to one side and constant terms to the other side. x - 6x = -18 -5x = -18

Step 3: Solve for "x" by dividing both sides by -5. x = (-18) / (-5) x = 18/5 x = 3.6

2. Equation 2: 1/2(4x - 2) = -7

Step 1: Distribute the 1/2 to the terms inside the parentheses. (1/2) * 4x - (1/2) * 2 = -7 2x - 1 = -7

Step 2: Move the constant term to the other side of the equation. 2x = -7 + 1 2x = -6

Step 3: Solve for "x" by dividing both sides by 2. x = -6 / 2 x = -3

So, the solutions for the given equations are x = 3.6 and x = -3.