The phrase “express in terms of ” asks you to solve for a variable: leave alone while stays in the formula. A positive test value in Desmos can catch a wrong choice, but one test cannot prove a formula works for every . To get the formula, distribute across both terms, then keep the equation balanced as you isolate .
Hints
- Hint 1
Choose a positive test value for , such as . A correct formula must give the same that the original equation gives. What does Desmos find when you substitute that value?
- Hint 2
To distribute the , multiply both terms inside the parentheses by it. In particular, multiplies as well as . What does the left side become?
- Hint 3
Use the balance rule: doing the same operation to both sides keeps an equation true. Once you have , what must you add to remove the ?
Step-by-step
Check a value, then isolate x
Step 1Find a test value in Desmos
Choose , which meets the positive-number condition. Type : tells Desmos which value to find, and tells it to fit the two sides. Under PARAMETERS, Desmos shows . Any correct formula must give when , but one test is a check, not proof for every .
- Step 2
Distribute the 5
Multiply by each term in ; it turns into :
- Step 3
Remove the minus 10
Add to both sides so that stands alone on the left: . The is the given plus the you added.
- Step 4
Get x alone
Divide both sides by : . This expresses in terms of , as requested. Choice D.