Question Solve the linear equation $9(x+2)=5-2(x-1)$ and select the correct solution.

Studdy Solution

STEP 1

1. The equation $9(x+2)=5-2(x-1)$ is a linear equation in one variable, $x$ .
2. To solve for $x$ , we will use algebraic manipulation to isolate $x$ on one side of the equation.
3. The solution will be one of the given options.

STEP 2

1. Distribute the multiplication on both sides of the equation.
2. Combine like terms.
3. Isolate the variable $x$ on one side of the equation.
4. Solve for $x$ and identify the correct option from the given choices.

STEP 3

Distribute the multiplication on both sides of the equation.
$9(x+2) = 5 - 2(x-1)$ $9x + 18 = 5 - 2x + 2$

STEP 4

Combine like terms on both sides of the equation.
$9x + 18 = 7 - 2x$

STEP 5

Add $2x$ to both sides of the equation to start isolating $x$ .
$9x + 2x + 18 = 7$

STEP 6

Combine the $x$ terms on the left side of the equation.
$11x + 18 = 7$

STEP 7

Subtract $18$ from both sides of the equation to further isolate $x$ .
$11x = 7 - 18$

STEP 8

Combine the constants on the right side of the equation.
$11x = -11$

STEP 9

Divide both sides of the equation by $11$ to solve for $x$ .
$x = \frac{-11}{11}$

STEP 10

Simplify the fraction to find the value of $x$ .
$x = -1$
The solution to the equation $9(x+2)=5-2(x-1)$ is $x = -1$ , which corresponds to option 2.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms