AB = 5x + 7 and CD = 13x - 10. Write and solve an equation to find x, AB and CD. Show all your steps in mathematical format
To find the value of x, we can set AB equal to CD and solve for x.
AB = CD
5x + 7 = 13x - 10
To isolate x, we can subtract 5x from both sides of the equation:
7 = 8x - 10
Next, we can add 10 to both sides of the equation:
17 = 8x
Finally, we can divide both sides of the equation by 8 to solve for x:
x = 17/8
Now that we have the value of x, we can substitute it back into one of the original equations to find the lengths of AB and CD.
Using the equation AB = 5x + 7:
AB = 5(17/8) + 7
AB = 85/8 + 56/8
AB = 141/8
AB = 17.625
Therefore, x is equal to 17/8, AB is equal to 17.625, and CD is equal to 13(17/8) - 10.