QuestionSolve for $x$ : $-7 x-(x+6)=9+2 x$
Answer Attempt 1 out of 2 $x=$ $\square$ Submit Answer

Studdy Solution

STEP 1

1. The equation is linear and can be solved for $x$ .
2. The equation involves combining like terms and using basic algebraic operations.
3. The solution will be a single value for $x$ .

STEP 2

1. Simplify the equation by distributing and combining like terms.
2. Move all terms involving $x$ to one side of the equation.
3. Isolate the variable $x$ .
4. Solve for $x$ .

STEP 3

Start by distributing the negative sign in the expression $-(x + 6)$ :
$-7x - x - 6 = 9 + 2x$

STEP 4

Combine like terms on the left side of the equation:
$-7x - x = -8x$
So the equation becomes:
$-8x - 6 = 9 + 2x$

STEP 5

Move all terms involving $x$ to one side by adding $8x$ to both sides:
$-8x + 8x - 6 = 9 + 2x + 8x$
Simplifying gives:
$-6 = 9 + 10x$

STEP 6

Isolate $x$ by moving the constant term to the other side. Subtract 9 from both sides:
$-6 - 9 = 10x$
Simplifying gives:
$-15 = 10x$

STEP 7

Solve for $x$ by dividing both sides by 10:
$x = \frac{-15}{10}$
Simplify the fraction:
$x = -\frac{3}{2}$
The solution is:
$\boxed{-\frac{3}{2}}$

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