Two less than 4 times a number is the same as the number plus 34. Find the number?

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Answer 1 · 2018-02-23T11:21:11

The required number is $12$ $12$ .

To solve the problem first define a variable for the required number.
Let's say, $n$ $n$ is our required number.

Then according to the given statement, we have:

$4 x - 2 = x + 34$ $4x-2=x+34$

Add $2$ $2$ to both sides:

$4 x - 2 + 2 = x + 34 + 2$ $4x-2+2=x+34+2$

$4 x = x + 36$ $4x=x+36$

Subtract $x$ $x$ from both sides:

$4 x - x = x + 36 - x$ $4x-x=x+36-x$

$3 x = 36$ $3x=36$

Divide both sides by $3$ $3$ :

$\frac{3 x}{3} = \frac{36}{3}$ $\frac{3x}{3}=\frac{36}{3}$

$x = 12$ $x=12$

That's it!

Answer 2 · 2018-02-23T11:26:27

The number is $12$ $12$

The phase "is the same as" separates the sentence into two equal parts.
Write an expression for each.

Let ' the number' be $x$ $x$

$4$ $4$ times the number : $4 x$ $4x$

Two less than that means: $4 x - 2$ $color(blue)(4x-2)$

The number plus $34$ $34$ is written as $x + 34$ $color(red)(x+34)$

These two expressions are equal to each other.

$4 x - 2 = x + 34$ $color(blue)(4x-2)" = "color(red)(x+34)$

$4 x - x = 34 + 2$ $4x -x = 34+2$

$3 x = 36$ $3x =36$

$x = 12$ $x =12$

Check:

$4 x - 2 = x + 34$ $color(blue)(4x-2)" = "color(red)(x+34)$

$4 (12) - 2 = (12) + 34$ $color(blue)(4(12)-2)" = "color(red)((12)+34)$

$46 = 46$ $color(blue)(46)" = "color(red)(46)$