Solved on Dec 07, 2023

Find the equation for the problem: When 296 is decreased by $11x$ , the result is 21. Solve for $x$ and check two answers.

STEP 1

Assumptions
1. The initial number is 296.
2. The number is decreased by 11 times an unknown number, which we will call $x$ .
3. The result after decreasing is 21.

STEP 2

We need to translate the word problem into an equation. The phrase "decreased by 11 times a number" means we subtract 11 times the unknown number from 296.
$296 - 11x = 21$

STEP 3

To solve for $x$ , we first isolate the term containing $x$ by subtracting 296 from both sides of the equation.
$296 - 11x - 296 = 21 - 296$

STEP 4

Simplify both sides of the equation.
$-11x = -275$

STEP 5

Now, we divide both sides by -11 to solve for $x$ .
$\frac{-11x}{-11} = \frac{-275}{-11}$

STEP 6

Calculate the value of $x$ .
$x = 25$

STEP 7

To check the solution, we substitute $x = 25$ back into the original equation to see if the result is 21.
$296 - 11 \times 25 = 21$

STEP 8

Calculate the left side of the equation.
$296 - 11 \times 25 = 296 - 275$

STEP 9

Simplify the expression.
$296 - 275 = 21$

STEP 10

Since the left side equals the right side (21 = 21), our solution $x = 25$ is correct.
The equation for the word problem is $296 - 11x = 21$ , and the solution for $x$ is 25.

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Find the equation for the problem: When 296 is decreased by $11x$ , the result is 21. Solve for $x$ and check two answers.

STEP 1

Assumptions
1. The initial number is 296.
2. The number is decreased by 11 times an unknown number, which we will call $x$ .
3. The result after decreasing is 21.

STEP 2

We need to translate the word problem into an equation. The phrase "decreased by 11 times a number" means we subtract 11 times the unknown number from 296.
$296 - 11x = 21$

STEP 3

To solve for $x$ , we first isolate the term containing $x$ by subtracting 296 from both sides of the equation.
$296 - 11x - 296 = 21 - 296$

STEP 4

Simplify both sides of the equation.
$-11x = -275$

STEP 5

Now, we divide both sides by -11 to solve for $x$ .
$\frac{-11x}{-11} = \frac{-275}{-11}$

STEP 6

Calculate the value of $x$ .
$x = 25$

STEP 7

To check the solution, we substitute $x = 25$ back into the original equation to see if the result is 21.
$296 - 11 \times 25 = 21$

STEP 8

Calculate the left side of the equation.
$296 - 11 \times 25 = 296 - 275$

STEP 9

Simplify the expression.
$296 - 275 = 21$

STEP 10

Since the left side equals the right side (21 = 21), our solution $x = 25$ is correct.
The equation for the word problem is $296 - 11x = 21$ , and the solution for $x$ is 25.

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Find the equation for the problem: When 296 is decreased by 11x11x11x, the result is 21. Solve for xxx and check two answers.

STEP 1

Assumptions1. The initial number is 296.2. The number is decreased by 11 times an unknown number, which we will call x x x.3. The result after decreasing is 21.

STEP 2

We need to translate the word problem into an equation. The phrase "decreased by 11 times a number" means we subtract 11 times the unknown number from 296.296−11x=21296 - 11x = 21296−11x=21

STEP 3

To solve for x x x, we first isolate the term containing x x x by subtracting 296 from both sides of the equation.296−11x−296=21−296296 - 11x - 296 = 21 - 296296−11x−296=21−296

STEP 4

Simplify both sides of the equation.−11x=−275-11x = -275−11x=−275

STEP 5

Now, we divide both sides by -11 to solve for x x x.−11x−11=−275−11\frac{-11x}{-11} = \frac{-275}{-11}−11−11x​=−11−275​

STEP 6

Calculate the value of x x x.x=25x = 25x=25

STEP 7

To check the solution, we substitute x=25 x = 25 x=25 back into the original equation to see if the result is 21.296−11×25=21296 - 11 \times 25 = 21296−11×25=21

STEP 8

Calculate the left side of the equation.296−11×25=296−275296 - 11 \times 25 = 296 - 275296−11×25=296−275

STEP 9

Simplify the expression.296−275=21296 - 275 = 21296−275=21

STEP 10

Since the left side equals the right side (21 = 21), our solution x=25 x = 25 x=25 is correct.The equation for the word problem is 296−11x=21 296 - 11x = 21 296−11x=21, and the solution for x x x is 25.

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

Find the equation for the problem: When 296 is decreased by $11x$ , the result is 21. Solve for $x$ and check two answers.

Assumptions
1. The initial number is 296.
2. The number is decreased by 11 times an unknown number, which we will call $x$ .
3. The result after decreasing is 21.

We need to translate the word problem into an equation. The phrase "decreased by 11 times a number" means we subtract 11 times the unknown number from 296.
$296 - 11x = 21$

To solve for $x$ , we first isolate the term containing $x$ by subtracting 296 from both sides of the equation.
$296 - 11x - 296 = 21 - 296$

Simplify both sides of the equation.
$-11x = -275$

Now, we divide both sides by -11 to solve for $x$ .
$\frac{-11x}{-11} = \frac{-275}{-11}$

Calculate the value of $x$ .
$x = 25$

To check the solution, we substitute $x = 25$ back into the original equation to see if the result is 21.
$296 - 11 \times 25 = 21$

Calculate the left side of the equation.
$296 - 11 \times 25 = 296 - 275$

Simplify the expression.
$296 - 275 = 21$

Since the left side equals the right side (21 = 21), our solution $x = 25$ is correct.
The equation for the word problem is $296 - 11x = 21$ , and the solution for $x$ is 25.