QuestionSolve for x in the equation: 3x - [8 - 3(x - 1)] = x + 19. Describe each step.

Studdy Solution

STEP 1

Assumptions1. We are given the equation $3x-[8-3(x-1)]=x+19$ . . The goal is to solve for $x$ .

STEP 2

First, we need to simplify the equation. We can start by distributing the $-$ inside the brackets to the terms $(x-1)$ .
$x - [8 -(x-1)] =x - [8 -x +]$

STEP 3

Next, we simplify the terms inside the brackets.
$3x - [8 -3x +3] =3x - [-3x +11]$

STEP 4

Now, we distribute the negative sign outside the brackets to the terms inside the brackets.
$3x - [-3x +11] =3x +3x -11$

STEP 5

Combine like terms on the left side of the equation.
$3x +3x -11 =x -11$

STEP 6

Now, we have simplified the left side of the equation. The equation now is $6x -11 = x +19$

STEP 7

To isolate $x$ , we need to get rid of the $x$ on the right side of the equation. We do this by subtracting $x$ from both sides of the equation.
$6x - x -11 = x - x +19$

STEP 8

implify the equation by performing the subtraction on both sides.
$5x -11 =19$

STEP 9

Next, we need to get rid of the $-11$ on the left side of the equation. We do this by adding $11$ to both sides of the equation.
$5x -11 +11 =19 +11$

STEP 10

implify the equation by performing the addition on both sides.
$5x =30$

STEP 11

Finally, to solve for $x$ , we divide both sides of the equation by $5$ .
$\frac{5x}{5} = \frac{30}{5}$

STEP 12

Perform the division to find the value of $x$ .
$x =6$ So, the solution to the equation is $x =6$ .

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