Work out the value of [tex]$u$[/tex]
[tex]$6 u=22-5 u$[/tex]
Answer (1)
Add 5 u to both sides of the equation: 6 u + 5 u = 22 − 5 u + 5 u .
Simplify the equation: 11 u = 22 .
Divide both sides by 11: u = 11 22 .
Simplify to find the value of u : u = 2 . The final answer is 2 .
Explanation
Understanding the Problem We are given the equation 6 u = 22 − 5 u and we want to find the value of u that satisfies this equation.
Isolating u Terms To solve for u , we first want to get all the terms with u on one side of the equation. We can do this by adding 5 u to both sides of the equation: 6 u + 5 u = 22 − 5 u + 5 u
Simplifying the Equation Now, we simplify both sides of the equation: 11 u = 22
Solving for u To isolate u , we divide both sides of the equation by 11: u = 11 22 u = 2
Final Answer Therefore, the value of u that satisfies the equation 6 u = 22 − 5 u is 2.
Examples
Imagine you're balancing a seesaw. On one side, you have 6 boxes labeled 'u', and on the other side, you have 22 blocks minus 5 boxes labeled 'u'. To find out how many blocks each 'u' box represents to balance the seesaw, you solve the equation 6 u = 22 − 5 u . This type of problem is also useful in scenarios like determining the break-even point in business, where costs equal revenue, or in physics, when calculating equilibrium forces.
