4y-3=10y+45

Question

solve the equation. be sure to check your proposed solution by substituting it for the variable in the original equation 

Answer 1

y=-8

4y-3 = 10y+45

Here's a graphical method for solving it. Not that you'd do this, but it gives an alternative to the usual algebra approach, and provides a check on the solution.

Let's change y to x and graph it

4x-3 = 10x+45

Graph each side and see where they intersect

Left side has slope = 4 with y-intercept of -3

right side has slope of 10 and y-intercept of 45

Just a rough sketch shows they intersect where x is negative.

the right side is steeper and crossing the y-axis higher. It can never intersect the smaller sloped line with the smaller y intercept

the solution is a negative number

Graph it more carefully and you can get the exact solution of -8 or the point (-8,-35). The two lines intersect in Quadrant III. since we switched x and y, y=-8 is the solution to the original problem.

Or

You can do the algebra

4y-3 = 10y+45

subtract 45 from both sides, subtract 4y from both sides to get

-48=6y

divide both sides by 6

-48/6 = -8 = y

y=-8

check the answer

4(-8)-3 = 10(-8)+45

-32-3 = -80+45

-35 = -35

Answer 2

4y - 3 = 10y + 45                   Given

4y - 3 + 3 = 10y + 45 + 3       Add 3 to each side

4y = 10y + 48                        Simplify each side

4y - 10y = 10y + 48 - 10y       Subtract 10y from each side

-6y = 48                               Simplify each side

-6y/(-6) = 48/(-6)                  Divide each side by -6

y = -8                                   Simplify each side

To check the problem, just substitute the answer (-8) in for y in the original equation

4(-8) - 3 = 10(-8) + 45

-32 - 3 = -80 + 45

-35 = -35

Since the final statement came out correctly, we know that the solution checked.