**Middle School Number Sense Lesson 101: Solving for X with a Ratio**

This concept is an extension of

**SolveX**, but with a specific format. It has shown up

**4 times**this year, with a median placement at

**question # 41**.

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**Number Dojo Level: 126**

The thing to look for with these problems is some kind of ratio relationship between x and a number. I approach the problems by cross-multiplying. It will be easier to explain with some examples.

**Example 1: If 7/(4x - 1)**

**= 1/9**

**, then x = ___**

- Cross-multiply the values intersecting at the = sign:
**(7)(9) = (4x – 1)(1)** - 63 = 4x – 1, so 64 = 4x.
- x = =
**16**

**Example 2: If 3/(x - 2)**

**= 1/2**

**, then x = ___**

- Cross-multiply:
**(3)(2) = (x – 2)(1)** - 6 = x – 2, so x =
**8**

**Example 3: If 4/x**

**= 7/3**

**, then x = ___**

- Cross –multiply:
**(4)(3) = (x)(7)** - 12 = 7x, so x =
**12/7**

**Example 4: If 4/(x - 3)**

**= 2/7**

**, then x = ___**

- Cross-multiply:
**(4)(7) = (x – 3)(2)** - 28 = 2x – 6, so 34 = 2x.
- x = =
**17**

**Example 5: If 3/x**

**= x/27**

**and x =>**

**0, then x = ___**

- Cross-multiply:
**(3)(27) = (x)(x)** - 81 = (x)(x) and x => 0, so x =
**9**

**Up Next for Middle School: SlopeLine2Pts**