How do you solve 1/2z+1/3=-2/512z+13=25?

2 Answers
Apr 23, 2017

See the entire solution process below:

Explanation:

First, multiply each side of the equation by color(red)(30)30 to eliminate the fractions while keeping the equation balanced. color(red)(3)3 is the Lowest Common Denominator of the three fractions:

color(red)(30)(1/2z + 1/3) = color(red)(30) * -2/530(12z+13)=3025

(color(red)(30) * 1/2z) + (color(red)(30) * 1/3) = cancel(color(red)(30))6 * -2/color(red)(cancel(color(black)(5)))

(cancel(color(red)(30)) 15 * 1/color(red)(cancel(color(black)(2)))z) + (cancel(color(red)(30)) 10 * 1/color(red)(cancel(color(black)(3)))) = 6 * -2

(15 * 1z) + (10 * 1) = -12

15z + 10 = -12

Next, subtract color(red)(10) from each side of the equation to isolate the z term while keeping the equation balanced:

15z + 10 - color(red)(10) = -12 - color(red)(10)

15z + 0 = -22

15z = -22

Now, divide each side of the equation by color(red)(15) to solve for z while keeping the equation balanced:

(15z)/color(red)(15) = -22/color(red)(15)

(color(red)(cancel(color(black)(15)))z)/cancel(color(red)(15)) = -22/15

z = -22/15

Apr 23, 2017

z=-22/15

Explanation:

First, let's multiply all terms by 30 to remove the fractions.
Doing this, we get:
15z+10=-12

Then, we simplify.
15z=-22

z=-22/15