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## SAT

### Course: SAT > Unit 6

Lesson 4: Passport to Advanced Math: lessons by skill- Solving quadratic equations | Lesson
- Interpreting nonlinear expressions | Lesson
- Quadratic and exponential word problems | Lesson
- Manipulating quadratic and exponential expressions | Lesson
- Radicals and rational exponents | Lesson
- Radical and rational equations | Lesson
- Operations with rational expressions | Lesson
- Operations with polynomials | Lesson
- Polynomial factors and graphs | Lesson
- Graphing quadratic functions | Lesson
- Graphing exponential functions | Lesson
- Linear and quadratic systems | Lesson
- Structure in expressions | Lesson
- Isolating quantities | Lesson
- Function Notation | Lesson

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# Isolating quantities | Lesson

## What is "Isolating quantities" and how frequently do these questions appear on the test?

Many real-world scenarios can be described using equations and formulas with multiple variables. For example, the formula for the area, A, of a rectangle with length ell and width w is A, equals, ell, w. In this form, area (A) is

**isolated**: it is alone on one side of the equation.If we wanted to find the equivalent equation, but with ell

**isolated**, we could divide both sides of the equation by w, giving us ell, equals, start fraction, A, divided by, w, end fraction.On your official SAT, you'll likely see

**0 to 2 questions**that test your ability to isolate a variable in an equation with two or more variables.**You can learn anything. Let's do this!**

## How do I isolate quantities?

### Manipulating formulas: temperature

### Like solving equations, but with more variables

Isolating quantities is similar to solving equations. However, instead of ending up with a variable equal to a constant, we end up with a variable equal to an expression containing other variables. In fact, if you've rewritten a linear equation like x, plus, y, equals, 1 in slope-intercept form, then you've already isolated y by rearranging a linear equation!

The most important thing to remember is that the rearranged equation will remain equivalent to the original equation

*only if*we always treat both sides equally: whenever we do something to one side, we*must*do the exact same thing to the other side.To isolate a quantity in an equation or formula:

- Write down the original equation. If needed, translate the word problem or given context into an equation.
- Perform the same operation on both sides of the equation to begin isolating the desired quantity.
- Repeat Step 2 until the desired quantity is isolated.

#### Let's look at some examples!

A physics student uses the formula E, start subscript, start text, k, end text, end subscript, equals, start fraction, 1, divided by, 2, end fraction, m, v, squared to calculate the kinetic energy in joules, E, start subscript, start text, k, end text, end subscript, of an object with a mass of m kilograms traveling at a speed of v meters per second. What is v in terms of E, start subscript, start text, k, end text, end subscript and m ?

The distance d traveled by an object moving at constant velocity is found by multiplying the velocity v of the subject by time t. Write an equation that gives the time t in terms of d and v.

### Try it!

## Your turn!

## Want to join the conversation?

- These questions seem pretty basic to me.

So I'm skeptical about having these questions in SAT.(7 votes)- Take a look through some practice tests. Tests 5, 6, 7, and 8 were all used as actual SAT tests, and they should have multiple of these "solve for a variable" questions per math section. A lot of SAT questions do indeed seem basic once you get to know them, and that's because they are. They can just seem intimidating to some test-takers because they haven't seen the equation before, or don't know what to do with so many letters and variables instead of a numerical expression.(12 votes)