Home > Algebra > Equations with Variables on Both Sides

How do you solve #\frac { x - 2} { 5} = \frac { 2x - 1} { 11}#?

Answer 1

Nathan Axel

#x = 17#

Multiply the left-hand numerator #(x -2)# by #11#. Multiply the right-hand numerator #(2x-1)# by #5#.

#11x-22=10x -5#

#11x-22-10x=10x -5-10x#

#x - 22 = -5#

#x - 22+22 = -5+22#

# x= 17#

You can substitute #17# in to original equation to check:

# (17-2)/5 =(17xx2-1)/11 #

# 3=3#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eva Abramson

To solve the equation (\frac{x - 2}{5} = \frac{2x - 1}{11}), you can follow these steps:

Cross multiply to eliminate the fractions.
Solve for (x).
Check your solution.

Cross multiplying, we get: [11(x - 2) = 5(2x - 1)]

Expanding both sides: [11x - 22 = 10x - 5]

Group like terms: [11x - 10x = 22 - 5]

Simplify: [x = 17]

Finally, check if (x = 17) satisfies the original equation: [\frac{17 - 2}{5} = \frac{2(17) - 1}{11}] [\frac{15}{5} = \frac{33 - 1}{11}] [3 = \frac{32}{11}]

Since the equation holds true, (x = 17) is the solution.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.